Optimize

Executioner for optimization problems.

Overview

This is executioner performs optimization using the TAO optimization toolkit. The specific algorithm used is specified using the "tao_solver" parameter. The options and connection with TAO algorithms is shown in Table 1. Additional solver options can be given to the TAO solver using the "petsc_options", "petsc_options_iname", and "petsc_options_value" parameters or from command-line.

Table 1: List of available optimization algorithms

Algorithm	"tao_solver"	TAO Option	`tao_type`
Newton Trust Region	`taontr`	TAONTR	`ntr`
Bounded Newton Trust Region	`taobntr`	TAOBNTR	`bntr`
Bounded Conjugate Gradient	`taobncg`	TAOBNCG	`bncg`
Newton Line Search	`taonls`	TAONLS	`nls`
Bounded Newton Line Search	`taobnls`	TAOBNLS	`bnls`
Limited Memory Variable Metric	`taolmvm`	TAOLMVM	`lmvm`
Bounded Limited Memory Variable Metric	`taoblmvm`	TAOBLMVM	`blmvm`
Nelder-Mead	`taonm`	TAONM	`nm`
Bounded Quasi-Newton Line Search	`taobqnls`	TAOBQNLS	`bqnls`
Orthant-wise Limited Memory	`taoowlqn`	TAOOWLQN	`taoowlqn`
Gradient Projection Conjugate Gradient	`taogpcg`	TAOGPCG	`gpcg`
Bundle Method for Regularized Risk Minimization	`taobmrm`	TAOBMRM	`bmrm`
Augmented Lagrangian Multiplier Method	`taoalmm`	TAOALMM	`almm`

This executioner relies on a OptimizationReporter to define the constraints, bounds, objective, and gradient of the form function. The objective is defined by the computeObjective member in the OptimizationReporter class. The gradient is defined by computeGradient and the bounds are defined by getUpperBounds and getLowerBounds. Whether it is necessary to define each of these members is based on whether the selected algorithm needs it, see Summary of Tao Solvers for more information. The Hessian is computed using a matrix-free method, where it evaluates the action of the Hessian on the form function parameters (the values that are being optimized). It does this by evaluating a homogeneous version of the objective function and subsequently computes the gradient. For constrained optimization the taoalmm algorithm needs to be used. When the taoalmm algorithm is selected the necessary methods for that algorithm are generated and only in an OptimizationReporter does the user need to provide the type and number of constraints.

To aid in the computation of the objective, gradient, and Hessian, this executioner includes additional execution flags that MOOSE objects (like MultiApps) can be evaluated on. Having execute_on = forward will execute the object(s) just before computeObjective is called and execute_on = adjoint will execute the object()s just before computeGradient is called. Having execute_on = homogeneous_forward will execute the object(s) during the matrix-free Hessian computation, before calling adjoint and computeGradient.

The form function's parameters are represented as a vector of values and is tied to reporter values within the OptimizationReporter.

Example Input Syntax

The following performs optimization using th Newton line search algorithm. The additional options set the optimization tolerance to $var element = document.getElementById("moose-equation-a05b00ec-2daa-4039-8d96-ebffac4026f5");katex.render("10^{-5}", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ , set the max iterations to 10, and set the linear solver type to conjugate gradient with no preconditioning.

[Executioner]
  type = Optimize
  tao_solver = taonls
  petsc_options_iname = '-tao_gttol -tao_max_it -tao_nls_pc_type -tao_nls_ksp_type'
  petsc_options_value = '1e-5 10 none cg'
  verbose = true
[]

Input Parameters

tao_solverTao solver to use for optimization.
C++ Type:MooseEnum
Unit:(no unit assumed)
Options:taontr, taobntr, taobncg, taonls, taobnls, taobqnktr, taontl, taobntl, taolmvm, taoblmvm, taonm, taobqnls, taoowlqn, taogpcg, taobmrm, taoalmm
Controllable:No
Description:Tao solver to use for optimization.

Required Parameters

output_optimization_iterationsFalseUse the time step as the current iteration for outputting optimization history.
Default:False
C++ Type:bool
Unit:(no unit assumed)
Controllable:No
Description:Use the time step as the current iteration for outputting optimization history.
solve_onFORWARD ADJOINT HOMOGENEOUS_FORWARDList of flags indicating when inner system solve should occur.
Default:FORWARD ADJOINT HOMOGENEOUS_FORWARD
C++ Type:ExecFlagEnum
Unit:(no unit assumed)
Options:FORWARD, ADJOINT, HOMOGENEOUS_FORWARD, NONE
Controllable:No
Description:List of flags indicating when inner system solve should occur.
time0System time
Default:0
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:System time
verboseFalseSet to true to print additional information
Default:False
C++ Type:bool
Unit:(no unit assumed)
Controllable:No
Description:Set to true to print additional information

Optional Parameters

accept_on_max_fixed_point_iterationFalseTrue to treat reaching the maximum number of fixed point iterations as converged.
Default:False
C++ Type:bool
Unit:(no unit assumed)
Controllable:No
Description:True to treat reaching the maximum number of fixed point iterations as converged.
auto_advanceFalseWhether to automatically advance sub-applications regardless of whether their solve converges, for transient executioners only.
Default:False
C++ Type:bool
Unit:(no unit assumed)
Controllable:No
Description:Whether to automatically advance sub-applications regardless of whether their solve converges, for transient executioners only.
custom_abs_tol1e-50The absolute nonlinear residual to shoot for during fixed point iterations. This check is performed based on postprocessor defined by the custom_pp residual.
Default:1e-50
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:The absolute nonlinear residual to shoot for during fixed point iterations. This check is performed based on postprocessor defined by the custom_pp residual.
custom_ppPostprocessor for custom fixed point convergence check.
C++ Type:PostprocessorName
Unit:(no unit assumed)
Controllable:No
Description:Postprocessor for custom fixed point convergence check.
custom_rel_tol1e-08The relative nonlinear residual drop to shoot for during fixed point iterations. This check is performed based on the postprocessor defined by custom_pp residual.
Default:1e-08
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:The relative nonlinear residual drop to shoot for during fixed point iterations. This check is performed based on the postprocessor defined by custom_pp residual.
direct_pp_valueFalseTrue to use direct postprocessor value (scaled by value on first iteration). False (default) to use difference in postprocessor value between fixed point iterations.
Default:False
C++ Type:bool
Unit:(no unit assumed)
Controllable:No
Description:True to use direct postprocessor value (scaled by value on first iteration). False (default) to use difference in postprocessor value between fixed point iterations.
disable_fixed_point_residual_norm_checkFalseDisable the residual norm evaluation thus the three parameters fixed_point_rel_tol, fixed_point_abs_tol and fixed_point_force_norms.
Default:False
C++ Type:bool
Unit:(no unit assumed)
Controllable:No
Description:Disable the residual norm evaluation thus the three parameters fixed_point_rel_tol, fixed_point_abs_tol and fixed_point_force_norms.
fixed_point_abs_tol1e-50The absolute nonlinear residual to shoot for during fixed point iterations. This check is performed based on the main app's nonlinear residual.
Default:1e-50
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:The absolute nonlinear residual to shoot for during fixed point iterations. This check is performed based on the main app's nonlinear residual.
fixed_point_algorithmpicardThe fixed point algorithm to converge the sequence of problems.
Default:picard
C++ Type:MooseEnum
Unit:(no unit assumed)
Options:picard, secant, steffensen
Controllable:No
Description:The fixed point algorithm to converge the sequence of problems.
fixed_point_force_normsFalseForce the evaluation of both the TIMESTEP_BEGIN and TIMESTEP_END norms regardless of the existence of active MultiApps with those execute_on flags, default: false.
Default:False
C++ Type:bool
Unit:(no unit assumed)
Controllable:No
Description:Force the evaluation of both the TIMESTEP_BEGIN and TIMESTEP_END norms regardless of the existence of active MultiApps with those execute_on flags, default: false.
fixed_point_max_its1Specifies the maximum number of fixed point iterations.
Default:1
C++ Type:unsigned int
Unit:(no unit assumed)
Controllable:No
Description:Specifies the maximum number of fixed point iterations.
fixed_point_min_its1Specifies the minimum number of fixed point iterations.
Default:1
C++ Type:unsigned int
Unit:(no unit assumed)
Controllable:No
Description:Specifies the minimum number of fixed point iterations.
fixed_point_rel_tol1e-08The relative nonlinear residual drop to shoot for during fixed point iterations. This check is performed based on the main app's nonlinear residual.
Default:1e-08
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:The relative nonlinear residual drop to shoot for during fixed point iterations. This check is performed based on the main app's nonlinear residual.
relaxation_factor1Fraction of newly computed value to keep.Set between 0 and 2.
Default:1
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Fraction of newly computed value to keep.Set between 0 and 2.
transformed_postprocessorsList of main app postprocessors to transform during fixed point iterations
C++ Type:std::vector<PostprocessorName>
Unit:(no unit assumed)
Controllable:No
Description:List of main app postprocessors to transform during fixed point iterations
transformed_variablesList of main app variables to transform during fixed point iterations
C++ Type:std::vector<std::string>
Unit:(no unit assumed)
Controllable:No
Description:List of main app variables to transform during fixed point iterations

Fixed Point Iterations Parameters

automatic_scalingFalseWhether to use automatic scaling for the variables.
Default:False
C++ Type:bool
Unit:(no unit assumed)
Controllable:No
Description:Whether to use automatic scaling for the variables.
compute_scaling_onceTrueWhether the scaling factors should only be computed once at the beginning of the simulation through an extra Jacobian evaluation. If this is set to false, then the scaling factors will be computed during an extra Jacobian evaluation at the beginning of every time step.
Default:True
C++ Type:bool
Unit:(no unit assumed)
Controllable:No
Description:Whether the scaling factors should only be computed once at the beginning of the simulation through an extra Jacobian evaluation. If this is set to false, then the scaling factors will be computed during an extra Jacobian evaluation at the beginning of every time step.
ignore_variables_for_autoscalingList of variables that do not participate in autoscaling.
C++ Type:std::vector<std::string>
Unit:(no unit assumed)
Controllable:No
Description:List of variables that do not participate in autoscaling.
off_diagonals_in_auto_scalingFalseWhether to consider off-diagonals when determining automatic scaling factors.
Default:False
C++ Type:bool
Unit:(no unit assumed)
Controllable:No
Description:Whether to consider off-diagonals when determining automatic scaling factors.
resid_vs_jac_scaling_param0A parameter that indicates the weighting of the residual vs the Jacobian in determining variable scaling parameters. A value of 1 indicates pure residual-based scaling. A value of 0 indicates pure Jacobian-based scaling
Default:0
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:A parameter that indicates the weighting of the residual vs the Jacobian in determining variable scaling parameters. A value of 1 indicates pure residual-based scaling. A value of 0 indicates pure Jacobian-based scaling
scaling_group_variablesName of variables that are grouped together for determining scale factors. (Multiple groups can be provided, separated by semicolon)
C++ Type:std::vector<std::vector<std::string>>
Unit:(no unit assumed)
Controllable:No
Description:Name of variables that are grouped together for determining scale factors. (Multiple groups can be provided, separated by semicolon)

Solver Variable Scaling Parameters

contact_line_search_allowed_lambda_cuts2The number of times lambda is allowed to be cut in half in the contact line search. We recommend this number be roughly bounded by 0 <= allowed_lambda_cuts <= 3
Default:2
C++ Type:unsigned int
Unit:(no unit assumed)
Controllable:No
Description:The number of times lambda is allowed to be cut in half in the contact line search. We recommend this number be roughly bounded by 0 <= allowed_lambda_cuts <= 3
contact_line_search_ltolThe linear relative tolerance to be used while the contact state is changing between non-linear iterations. We recommend that this tolerance be looser than the standard linear tolerance
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:The linear relative tolerance to be used while the contact state is changing between non-linear iterations. We recommend that this tolerance be looser than the standard linear tolerance
line_searchdefaultSpecifies the line search type (Note: none = basic)
Default:default
C++ Type:MooseEnum
Unit:(no unit assumed)
Options:basic, bt, contact, cp, default, l2, none, project, shell
Controllable:No
Description:Specifies the line search type (Note: none = basic)
line_search_packagepetscThe solver package to use to conduct the line-search
Default:petsc
C++ Type:MooseEnum
Unit:(no unit assumed)
Options:petsc, moose
Controllable:No
Description:The solver package to use to conduct the line-search

Solver Line Search Parameters

control_tagsAdds user-defined labels for accessing object parameters via control logic.
C++ Type:std::vector<std::string>
Unit:(no unit assumed)
Controllable:No
Description:Adds user-defined labels for accessing object parameters via control logic.
enableTrueSet the enabled status of the MooseObject.
Default:True
C++ Type:bool
Unit:(no unit assumed)
Controllable:No
Description:Set the enabled status of the MooseObject.
outputsVector of output names where you would like to restrict the output of variables(s) associated with this object
C++ Type:std::vector<OutputName>
Unit:(no unit assumed)
Controllable:No
Description:Vector of output names where you would like to restrict the output of variables(s) associated with this object
skip_exception_checkFalseSpecifies whether or not to skip exception check
Default:False
C++ Type:bool
Unit:(no unit assumed)
Controllable:No
Description:Specifies whether or not to skip exception check

Advanced Parameters

l_abs_tol1e-50Linear Absolute Tolerance
Default:1e-50
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Linear Absolute Tolerance
l_max_its10000Max Linear Iterations
Default:10000
C++ Type:unsigned int
Unit:(no unit assumed)
Controllable:No
Description:Max Linear Iterations
l_tol1e-05Linear Relative Tolerance
Default:1e-05
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Linear Relative Tolerance
reuse_preconditionerFalseIf true reuse the previously calculated preconditioner for the linearized system across multiple solves spanning nonlinear iterations and time steps. The preconditioner resets as controlled by reuse_preconditioner_max_linear_its
Default:False
C++ Type:bool
Unit:(no unit assumed)
Controllable:No
Description:If true reuse the previously calculated preconditioner for the linearized system across multiple solves spanning nonlinear iterations and time steps. The preconditioner resets as controlled by reuse_preconditioner_max_linear_its
reuse_preconditioner_max_linear_its25Reuse the previously calculated preconditioner for the linear system until the number of linear iterations exceeds this number
Default:25
C++ Type:unsigned int
Unit:(no unit assumed)
Controllable:No
Description:Reuse the previously calculated preconditioner for the linear system until the number of linear iterations exceeds this number

Linear Solver Parameters

max_xfem_update4294967295Maximum number of times to update XFEM crack topology in a step due to evolving cracks
Default:4294967295
C++ Type:unsigned int
Unit:(no unit assumed)
Controllable:No
Description:Maximum number of times to update XFEM crack topology in a step due to evolving cracks
update_xfem_at_timestep_beginFalseShould XFEM update the mesh at the beginning of the timestep
Default:False
C++ Type:bool
Unit:(no unit assumed)
Controllable:No
Description:Should XFEM update the mesh at the beginning of the timestep

Xfem Fixed Point Iterations Parameters

mffd_typewpSpecifies the finite differencing type for Jacobian-free solve types. Note that the default is wp (for Walker and Pernice).
Default:wp
C++ Type:MooseEnum
Unit:(no unit assumed)
Options:wp, ds
Controllable:No
Description:Specifies the finite differencing type for Jacobian-free solve types. Note that the default is wp (for Walker and Pernice).
petsc_optionsSingleton PETSc options
C++ Type:MultiMooseEnum
Unit:(no unit assumed)
Options:-dm_moose_print_embedding, -dm_view, -ksp_converged_reason, -ksp_gmres_modifiedgramschmidt, -ksp_monitor, -ksp_monitor_snes_lg-snes_ksp_ew, -ksp_snes_ew, -snes_converged_reason, -snes_ksp, -snes_ksp_ew, -snes_linesearch_monitor, -snes_mf, -snes_mf_operator, -snes_monitor, -snes_test_display, -snes_view
Controllable:No
Description:Singleton PETSc options
petsc_options_inameNames of PETSc name/value pairs
C++ Type:MultiMooseEnum
Unit:(no unit assumed)
Options:-ksp_atol, -ksp_gmres_restart, -ksp_max_it, -ksp_pc_side, -ksp_rtol, -ksp_type, -mat_fd_coloring_err, -mat_fd_type, -mat_mffd_type, -pc_asm_overlap, -pc_factor_levels, -pc_factor_mat_ordering_type, -pc_hypre_boomeramg_grid_sweeps_all, -pc_hypre_boomeramg_max_iter, -pc_hypre_boomeramg_strong_threshold, -pc_hypre_type, -pc_type, -snes_atol, -snes_linesearch_type, -snes_ls, -snes_max_it, -snes_rtol, -snes_divergence_tolerance, -snes_type, -sub_ksp_type, -sub_pc_type
Controllable:No
Description:Names of PETSc name/value pairs
petsc_options_valueValues of PETSc name/value pairs (must correspond with "petsc_options_iname"
C++ Type:std::vector<std::string>
Unit:(no unit assumed)
Controllable:No
Description:Values of PETSc name/value pairs (must correspond with "petsc_options_iname"

Petsc Parameters

n_max_nonlinear_pingpong100The maximum number of times the nonlinear residual can ping pong before requesting halting the current evaluation and requesting timestep cut
Default:100
C++ Type:unsigned int
Unit:(no unit assumed)
Controllable:No
Description:The maximum number of times the nonlinear residual can ping pong before requesting halting the current evaluation and requesting timestep cut
nl_abs_div_tol1e+50Nonlinear Absolute Divergence Tolerance. A negative value disables this check.
Default:1e+50
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Nonlinear Absolute Divergence Tolerance. A negative value disables this check.
nl_abs_step_tol0Nonlinear Absolute step Tolerance
Default:0
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Nonlinear Absolute step Tolerance
nl_abs_tol1e-50Nonlinear Absolute Tolerance
Default:1e-50
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Nonlinear Absolute Tolerance
nl_div_tol1e+10Nonlinear Relative Divergence Tolerance. A negative value disables this check.
Default:1e+10
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Nonlinear Relative Divergence Tolerance. A negative value disables this check.
nl_forced_its0The Number of Forced Nonlinear Iterations
Default:0
C++ Type:unsigned int
Unit:(no unit assumed)
Controllable:No
Description:The Number of Forced Nonlinear Iterations
nl_max_funcs10000Max Nonlinear solver function evaluations
Default:10000
C++ Type:unsigned int
Unit:(no unit assumed)
Controllable:No
Description:Max Nonlinear solver function evaluations
nl_max_its50Max Nonlinear Iterations
Default:50
C++ Type:unsigned int
Unit:(no unit assumed)
Controllable:No
Description:Max Nonlinear Iterations
nl_rel_step_tol0Nonlinear Relative step Tolerance
Default:0
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Nonlinear Relative step Tolerance
nl_rel_tol1e-08Nonlinear Relative Tolerance
Default:1e-08
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Nonlinear Relative Tolerance
num_grids1The number of grids to use for a grid sequencing algorithm. This includes the final grid, so num_grids = 1 indicates just one solve in a time-step
Default:1
C++ Type:unsigned int
Unit:(no unit assumed)
Controllable:No
Description:The number of grids to use for a grid sequencing algorithm. This includes the final grid, so num_grids = 1 indicates just one solve in a time-step
residual_and_jacobian_togetherFalseWhether to compute the residual and Jacobian together.
Default:False
C++ Type:bool
Unit:(no unit assumed)
Controllable:No
Description:Whether to compute the residual and Jacobian together.
snesmf_reuse_baseTrueSpecifies whether or not to reuse the base vector for matrix-free calculation
Default:True
C++ Type:bool
Unit:(no unit assumed)
Controllable:No
Description:Specifies whether or not to reuse the base vector for matrix-free calculation
solve_typePJFNK: Preconditioned Jacobian-Free Newton Krylov JFNK: Jacobian-Free Newton Krylov NEWTON: Full Newton Solve FD: Use finite differences to compute Jacobian LINEAR: Solving a linear problem
C++ Type:MooseEnum
Unit:(no unit assumed)
Options:PJFNK, JFNK, NEWTON, FD, LINEAR
Controllable:No
Description:PJFNK: Preconditioned Jacobian-Free Newton Krylov JFNK: Jacobian-Free Newton Krylov NEWTON: Full Newton Solve FD: Use finite differences to compute Jacobian LINEAR: Solving a linear problem
splittingTop-level splitting defining a hierarchical decomposition into subsystems to help the solver.
C++ Type:std::vector<std::string>
Unit:(no unit assumed)
Controllable:No
Description:Top-level splitting defining a hierarchical decomposition into subsystems to help the solver.
use_pre_SMO_residualFalseCompute the pre-SMO residual norm and use it in the relative convergence check. The pre-SMO residual is computed at the begining of the time step before solution-modifying objects are executed. Solution-modifying objects include preset BCs, constraints, predictors, etc.
Default:False
C++ Type:bool
Unit:(no unit assumed)
Controllable:No
Description:Compute the pre-SMO residual norm and use it in the relative convergence check. The pre-SMO residual is computed at the begining of the time step before solution-modifying objects are executed. Solution-modifying objects include preset BCs, constraints, predictors, etc.

Nonlinear Solver Parameters

Restart Parameters

Input Files

(modules/optimization/test/tests/optimizationreporter/mesh_source/main.i)
(modules/optimization/test/tests/executioners/constrained/shape_optimization/main.i)
(modules/combined/test/tests/optimization/invOpt_mechanics/main_auto_adjoint.i)
(modules/optimization/test/tests/optimizationreporter/general_opt/point_loads_gen_opt/main_auto_adjoint_transfer_data.i)
(modules/optimization/test/tests/optimizationreporter/constant_heat_source/main.i)
(modules/optimization/test/tests/optimizationreporter/general_opt/point_loads_gen_opt/main_separate_multiapps.i)
(modules/optimization/test/tests/executioners/basic_optimize/debug_fd.i)
(modules/optimization/test/tests/optimizationreporter/constant_heat_source/main_nonLinear.i)
(modules/optimization/test/tests/optimizationreporter/bimaterial/main_auto_adjoint.i)
(modules/optimization/examples/simpleTransient/main_mesh.i)
(modules/optimization/test/tests/executioners/basic_optimize/debug_gradient.i)
(modules/optimization/test/tests/optimizationreporter/general_opt/point_loads_gen_opt/main_auto_adjoint.i)
(modules/optimization/test/tests/optimizationreporter/material/main.i)
(modules/optimization/test/tests/outputs/exodus_optimization_steady/main.i)
(modules/optimization/test/tests/executioners/constrained/inequality/main_auto_adjoint.i)
(modules/optimization/test/tests/optimizationreporter/mesh_source/main_auto_adjoint.i)
(modules/optimization/examples/materialTransient/optimize_auto_adjoint.i)
(modules/optimization/test/tests/optimizationreporter/point_loads/main.i)
(modules/optimization/test/tests/optimizationreporter/nonlinear_material/main.i)
(modules/optimization/examples/materialTransient/optimize_grad.i)
(modules/optimization/test/tests/optimizationreporter/general_opt/function_optimization/main.i)
(modules/optimization/test/tests/optimizationreporter/mesh_source/main_linearRestart.i)
(modules/optimization/examples/simpleTransient/main_auto_adjoint.i)
(modules/optimization/test/tests/executioners/constrained/equality/quadratic_minimize_constrained.i)
(modules/optimization/examples/diffusion_reaction/optimize.i)
(modules/optimization/test/tests/executioners/basic_optimize/qm_multi_param.i)
(modules/combined/test/tests/optimization/invOpt_bc_convective/main.i)
(modules/optimization/test/tests/executioners/basic_optimize/quadratic_minimize.i)
(modules/optimization/test/tests/optimizationreporter/bimaterial/main.i)
(modules/optimization/examples/materialFrequency/wave1D/inversion.i)
(modules/optimization/examples/materialTransient/optimize_nograd.i)
(modules/optimization/test/tests/optimizationreporter/bc_load_linearFunction/main.i)
(modules/combined/test/tests/optimization/invOpt_elasticity_modular/main.i)
(modules/optimization/test/tests/outputs/exodus_optimization_steady/main_auto_adjoint.i)
(modules/optimization/test/tests/optimizationreporter/bc_load_linearFunction/main_auto_adjoint.i)
(modules/optimization/test/tests/reporters/multiExperiment/optimize.i)
(modules/optimization/examples/simpleTransient/main_gradient.i)
(modules/combined/test/tests/optimization/invOpt_mechanics/main.i)
(modules/optimization/test/tests/optimizationreporter/point_loads/main_auto_adjoint.i)
(modules/combined/test/tests/optimization/invOpt_nonlinear/main.i)

(modules/optimization/include/optimizationreporters/OptimizationReporter.h)

// This file is part of the MOOSE framework
// https://www.mooseframework.org
//
// All rights reserved, see COPYRIGHT for full restrictions
// https://github.com/idaholab/moose/blob/master/COPYRIGHT
//
// Licensed under LGPL 2.1, please see LICENSE for details
// https://www.gnu.org/licenses/lgpl-2.1.html

#pragma once

#include "OptimizationData.h"
#include "OptimizationReporterBase.h"

/**
 * Computes gradient and contains reporters for communicating between optimizeSolve and subapps
 */
class OptimizationReporter : public OptimizationDataTempl<OptimizationReporterBase>
{

public:
  static InputParameters validParams();
  OptimizationReporter(const InputParameters & parameters);

  virtual Real computeObjective() override;
  virtual void setMisfitToSimulatedValues() override;

protected:
  virtual void setICsandBounds() override;
};

(modules/optimization/test/tests/optimizationreporter/point_loads/main.i)

# DO NOT CHANGE THIS TEST
# this test is documented as an example in forceInv_pointLoads.md
# if this test is changed, the figures will need to be updated.
measurement_points = '0.5 0.28 0
   0.5 0.6 0
   0.5 0.8 0
   0.5 1.1 0'
measurement_values = '293 304 315 320'
[Optimization]
[]

[OptimizationReporter]
  type = GeneralOptimization
  objective_name = objective_value
  parameter_names = 'parameter_results'
  num_values = '3'
[]

[Reporters]
  [main]
    type = OptimizationData
    measurement_points = ${measurement_points}
    measurement_values = ${measurement_values}
  []
[]

[Executioner]
  type = Optimize
  tao_solver = taonls
  petsc_options_iname = '-tao_gttol -tao_max_it -tao_nls_pc_type -tao_nls_ksp_type'
  petsc_options_value = '1e-5 10 none cg'
  verbose = true
[]

[MultiApps]
  [forward]
    type = FullSolveMultiApp
    input_files = forward.i
    execute_on = "FORWARD"
  []
  [adjoint]
    type = FullSolveMultiApp
    input_files = adjoint.i
    execute_on = "ADJOINT"
  []
  [homogeneousForward]
    type = FullSolveMultiApp
    input_files = forward_homogeneous.i
    execute_on = "HOMOGENEOUS_FORWARD"
  []
[]

[Transfers]
  # FORWARD transfers
  [toForward_measument]
    type = MultiAppReporterTransfer
    to_multi_app = forward
    from_reporters = 'main/measurement_xcoord
                      main/measurement_ycoord
                      main/measurement_zcoord
                      main/measurement_time
                      main/measurement_values
                      OptimizationReporter/parameter_results'
    to_reporters = 'measure_data/measurement_xcoord
                    measure_data/measurement_ycoord
                    measure_data/measurement_zcoord
                    measure_data/measurement_time
                    measure_data/measurement_values
                    point_source/value'
  []
  [fromForward]
    type = MultiAppReporterTransfer
    from_multi_app = forward
    # Note: We are transferring the misfit values into main misfit
    from_reporters = 'measure_data/objective_value measure_data/misfit_values'
    to_reporters = 'OptimizationReporter/objective_value main/misfit_values'
  []

  # ADJOINT transfers
  #NOTE:  the adjoint variable we are transferring is actually the gradient
  [toAdjoint]
    type = MultiAppReporterTransfer
    to_multi_app = adjoint
    from_reporters = 'main/measurement_xcoord
                      main/measurement_ycoord
                      main/measurement_zcoord
                      main/measurement_time
                      main/misfit_values'
    to_reporters = 'misfit/measurement_xcoord
                    misfit/measurement_ycoord
                    misfit/measurement_zcoord
                    misfit/measurement_time
                    misfit/misfit_values'
  []
  [fromAdjoint]
    type = MultiAppReporterTransfer
    from_multi_app = adjoint
    from_reporters = 'gradient/adjoint'
    to_reporters = 'OptimizationReporter/grad_parameter_results'
  []

  # HESSIAN transfers.  Same as forward.
  [toHomoForward]
    type = MultiAppReporterTransfer
    multi_app = homogeneousForward
    direction = to_multiapp
    from_reporters = 'main/measurement_xcoord
                      main/measurement_ycoord
                      main/measurement_zcoord
                      main/measurement_time
                      main/measurement_values
                      OptimizationReporter/parameter_results'
    to_reporters = 'measure_data/measurement_xcoord
                    measure_data/measurement_ycoord
                    measure_data/measurement_zcoord
                    measure_data/measurement_time
                    measure_data/measurement_values
                    point_source/value'
  []
  [fromHomoForward]
    type = MultiAppReporterTransfer
    multi_app = homogeneousForward
    direction = from_multiapp
    # Note: We are transferring the simulation values into misfit
    # this has to be done when using general opt and homogenous forward.
    from_reporters = 'measure_data/simulation_values'
    to_reporters = 'main/misfit_values'
  []
[]

[Reporters]
  [optInfo]
    type = OptimizationInfo
  []
[]

[Outputs]
  csv = true
[]

(modules/optimization/test/tests/optimizationreporter/mesh_source/main.i)

[Optimization]
[]

[OptimizationReporter]
  type = ParameterMeshOptimization
  objective_name = objective_value
  parameter_names = 'source'
  parameter_meshes = 'parameter_mesh_in.e'
[]

[Reporters]
  [main]
    type = OptimizationData
    # Random points
    measurement_points = '0.78193073 0.39115321 0
  0.72531893 0.14319403 0
  0.14052488 0.86976625 0
  0.401893   0.54241797 0
  0.02645427 0.43320192 0
  0.28856889 0.0035165  0
  0.51433644 0.94485949 0
  0.29252255 0.7962032  0
  0.04925654 0.58018889 0
  0.04717357 0.9556314  0'
    # sin(x*pi/2)*sin(y*pi/2)
    measurement_values = '0.54299466 0.20259611 0.21438235 0.44418597 0.02613676
  0.00241892 0.72014019 0.42096307 0.06108895 0.07385256'
  []
[]

[Executioner]
  type = Optimize
  tao_solver = taolmvm
  petsc_options_iname = '-tao_gatol'
  petsc_options_value = '1e-4'
  verbose = true
[]

[MultiApps]
  [forward]
    type = FullSolveMultiApp
    input_files = forward.i
    execute_on = FORWARD
  []
  [adjoint]
    type = FullSolveMultiApp
    input_files = adjoint.i
    execute_on = ADJOINT
  []
[]

[Transfers]
  [toForward_measument]
    type = MultiAppReporterTransfer
    to_multi_app = forward
    from_reporters = 'main/measurement_xcoord
                      main/measurement_ycoord
                      main/measurement_zcoord
                      main/measurement_time
                      main/measurement_values
                      OptimizationReporter/source'
    to_reporters = 'measure_data/measurement_xcoord
                    measure_data/measurement_ycoord
                    measure_data/measurement_zcoord
                    measure_data/measurement_time
                    measure_data/measurement_values
                    src_rep/vals'
  []
  [toAdjoint]
    type = MultiAppReporterTransfer
    to_multi_app = adjoint
    from_reporters = 'main/measurement_xcoord
                      main/measurement_ycoord
                      main/measurement_zcoord
                      main/measurement_time
                      main/misfit_values
                      OptimizationReporter/source'
    to_reporters = 'misfit/measurement_xcoord
                    misfit/measurement_ycoord
                    misfit/measurement_zcoord
                    misfit/measurement_time
                    misfit/misfit_values
                    src_rep/vals'
  []
  [fromForward]
    type = MultiAppReporterTransfer
    from_multi_app = forward
    from_reporters = 'measure_data/misfit_values measure_data/objective_value'
    to_reporters = 'main/misfit_values OptimizationReporter/objective_value'
  []
  [fromadjoint]
    type = MultiAppReporterTransfer
    from_multi_app = adjoint
    from_reporters = 'gradient_vpp/inner_product'
    to_reporters = 'OptimizationReporter/grad_source'
  []
[]

(modules/optimization/test/tests/executioners/constrained/shape_optimization/main.i)

[Optimization]
[]

[OptimizationReporter]
  type = GeneralOptimization
  parameter_names = 'radii'
  num_values_name = num_radii
  equality_names = 'volume_constraint'
  initial_condition = '0 0'
  lower_bounds = '-10'
  upper_bounds = '10'
  objective_name = max_temp
[]

[Executioner]
  type = Optimize
  tao_solver = taoalmm
  petsc_options_iname = '-tao_almm_subsolver_tao_type -tao_gatol -tao_catol  -tao_almm_type -tao_almm_mu_init -tao_fd_gradient -tao_fd_delta'
  petsc_options_value = 'bqnktr 1e-3 1e-3  phr 1e9 true 1e-8 '
  verbose = true
[]

[MultiApps]
  [forward]
    type = FullSolveMultiApp
    input_files = forward.i
    # Run on initial so the forward problem can determine number of parameters
    execute_on = 'INITIAL FORWARD'
  []
[]

[Transfers]
  [to_forward]
    type = MultiAppReporterTransfer
    to_multi_app = forward
    from_reporters = 'OptimizationReporter/radii'
    to_reporters = 'params/radii'
    execute_on = FORWARD
  []
  [from_forward]
    type = MultiAppReporterTransfer
    from_multi_app = forward
    from_reporters = 'params/num_params
                      objective/value
                      vol_constraint/vol_constraint
                      eq_grad/eq_grad'
    to_reporters = 'OptimizationReporter/num_radii
                    OptimizationReporter/max_temp
                    OptimizationReporter/volume_constraint
                    OptimizationReporter/grad_volume_constraint'
  []
[]

[Outputs]
  csv = true
  print_linear_residuals = false
  print_nonlinear_residuals = false
[]

(modules/combined/test/tests/optimization/invOpt_mechanics/main_auto_adjoint.i)

[Optimization]
[]

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 10
  ny = 2
  xmin = 0.0
  xmax = 5.0
  ymin = 0.0
  ymax = 1.0
[]

[OptimizationReporter]
  type = GeneralOptimization
  objective_name = objective_value
  parameter_names = 'force_right'
  num_values = '2'
  initial_condition = '100'
  outputs = 'csv'
[]

[Executioner]
  type = Optimize
  tao_solver = taobqnktr
  petsc_options_iname = '-tao_gttol -tao_max_it'
  petsc_options_value = '1e-7 500 '
  verbose = true
[]

[MultiApps]
  [forward]
    type = FullSolveMultiApp
    input_files = forward_and_adjoint.i
    execute_on = "FORWARD"
    clone_parent_mesh = true
  []
[]

[Transfers]
  [toForward_measument]
    type = MultiAppReporterTransfer
    to_multi_app = forward
    from_reporters = 'OptimizationReporter/force_right'
    to_reporters = 'params/right_values'
  []
  [fromForward]
    type = MultiAppReporterTransfer
    from_multi_app = forward
    from_reporters = 'combined/gradient obj/obj_val'
    to_reporters = 'OptimizationReporter/grad_force_right OptimizationReporter/objective_value'
  []
[]

[Outputs]
  csv = true
  execute_on = 'FINAL'
[]

(modules/optimization/test/tests/optimizationreporter/general_opt/point_loads_gen_opt/main_auto_adjoint_transfer_data.i)

[Optimization]
[]

[OptimizationReporter]
  type = GeneralOptimization
  objective_name = misfit_norm
  parameter_names = 'parameter_results'
  num_values = '3'
[]
[Reporters]
  [measure_data]
    type = OptimizationData
    measurement_points = '0.5 0.28 0
                          0.5 0.6 0
                          0.5 0.8 0
                          0.5 1.1 0'
    measurement_values = '293 304 315 320'
  []
[]

[Executioner]
  type = Optimize
  tao_solver = taolmvm
  petsc_options_iname = '-tao_gttol -tao_ls_type'
  petsc_options_value = '1e-5 unit'
  verbose = true
[]

[MultiApps]
  [forward]
    type = FullSolveMultiApp
    input_files = forward_and_adjoint_transfer_data.i
    execute_on = "FORWARD"
  []
[]

[Transfers]
  # FORWARD transfers
  [toForward_measument]
    type = MultiAppReporterTransfer
    to_multi_app = forward
    from_reporters = 'measure_data/measurement_xcoord
                      measure_data/measurement_ycoord
                      measure_data/measurement_zcoord
                      measure_data/measurement_time
                      measure_data/measurement_values
                      OptimizationReporter/parameter_results'
    to_reporters = 'measure_data/measurement_xcoord
                    measure_data/measurement_ycoord
                    measure_data/measurement_zcoord
                    measure_data/measurement_time
                    measure_data/measurement_values
                    point_source/value'
  []

  [fromForward]
    type = MultiAppReporterTransfer
    from_multi_app = forward
    from_reporters = 'gradient/temperature_adjoint
                      measure_data/misfit_norm'
    to_reporters = 'OptimizationReporter/grad_parameter_results
                    OptimizationReporter/misfit_norm'
  []
[]

[Outputs]
  csv = true
  file_base = main_out
[]

(modules/optimization/test/tests/optimizationreporter/constant_heat_source/main.i)

[Optimization]
[]

[OptimizationReporter]
  type = GeneralOptimization
  objective_name = objective_value
  parameter_names = 'parameter_results'
  num_values = '1'
  initial_condition = '500'
  lower_bounds = '0.1'
  upper_bounds = '10000'
[]

[Reporters]
  [main]
    type = OptimizationData
    measurement_points = '0.2 0.2 0
              0.8 0.6 0
              0.2 1.4 0
              0.8 1.8 0'
    measurement_values = '226 254 214 146'
  []
[]

[Executioner]
  type = Optimize
  tao_solver = taoblmvm
  petsc_options_iname = '-tao_gatol'
  petsc_options_value = '1e-6'
  verbose = true
[]

[MultiApps]
  [forward]
    type = FullSolveMultiApp
    input_files = forward.i
    execute_on = FORWARD
  []
  [adjoint]
    type = FullSolveMultiApp
    input_files = adjoint.i
    execute_on = ADJOINT
  []
[]

[Transfers]
  [toForward_measument]
    type = MultiAppReporterTransfer
    to_multi_app = forward
    from_reporters = 'main/measurement_xcoord
                      main/measurement_ycoord
                      main/measurement_zcoord
                      main/measurement_time
                      main/measurement_values
                      OptimizationReporter/parameter_results'
    to_reporters = 'measure_data/measurement_xcoord
                    measure_data/measurement_ycoord
                    measure_data/measurement_zcoord
                    measure_data/measurement_time
                    measure_data/measurement_values
                    params/q'
  []
  [toAdjoint]
    type = MultiAppReporterTransfer
    to_multi_app = adjoint
    from_reporters = 'main/measurement_xcoord
                      main/measurement_ycoord
                      main/measurement_zcoord
                      main/measurement_time
                      main/misfit_values
                      OptimizationReporter/parameter_results'
    to_reporters = 'misfit/measurement_xcoord
                    misfit/measurement_ycoord
                    misfit/measurement_zcoord
                    misfit/measurement_time
                    misfit/misfit_values
                    params/q'
  []
  [fromForward]
    type = MultiAppReporterTransfer
    from_multi_app = forward
    from_reporters = 'measure_data/misfit_values measure_data/objective_value'
    to_reporters = 'main/misfit_values OptimizationReporter/objective_value'
  []
  [fromadjoint]
    type = MultiAppReporterTransfer
    from_multi_app = adjoint
    from_reporters = 'gradient_vpp/inner_product'
    to_reporters = 'OptimizationReporter/grad_parameter_results'
  []
[]

[Outputs]
  csv = true
[]

(modules/optimization/test/tests/optimizationreporter/general_opt/point_loads_gen_opt/main_separate_multiapps.i)

measurement_points = '0.5 0.28 0
   0.5 0.6 0
   0.5 0.8 0
   0.5 1.1 0'
measurement_values = '293 304 315 320'

[Optimization]
[]

[OptimizationReporter]
  type = GeneralOptimization
  objective_name = misfit_norm
  parameter_names = 'parameter_results'
  num_values = '3'
[]
[Reporters]
  [main]
    # We need to have an OptimizationData on the main app to allow the
    # transferring of the correct information when doing Hessian based optimization.
    type = OptimizationData
    measurement_points = ${measurement_points}
    measurement_values = ${measurement_values}
  []
[]
[Executioner]
  type = Optimize
  tao_solver = taonls
  petsc_options_iname = '-tao_gttol -tao_max_it -tao_nls_pc_type -tao_nls_ksp_type'
  petsc_options_value = '1e-5 10 none cg'
  verbose = true
[]

[MultiApps]
  [forward]
    type = FullSolveMultiApp
    input_files = forward.i
    execute_on = "FORWARD"
    cli_args = 'measurement_points="${measurement_points}";measurement_values="${measurement_values}"'
  []
  [adjoint]
    type = FullSolveMultiApp
    input_files = adjoint.i
    execute_on = "ADJOINT"
    cli_args = 'measurement_points="${measurement_points}";measurement_values="${measurement_values}"'
  []
  [homogeneousForward]
    type = FullSolveMultiApp
    input_files = forward_homogeneous.i
    execute_on = "HOMOGENEOUS_FORWARD"
    cli_args = 'measurement_points="${measurement_points}";measurement_values="${measurement_values}"'
  []
[]

[Transfers]
  # FORWARD transfers
  [toForward_measument]
    type = MultiAppReporterTransfer
    to_multi_app = forward
    from_reporters = 'OptimizationReporter/parameter_results'
    to_reporters = 'point_source/value'
  []
  [fromForward]
    type = MultiAppReporterTransfer
    from_multi_app = forward
    # Note: We are transferring the misfit values into main misfit
    from_reporters = 'measure_data/misfit_norm measure_data/misfit_values'
    to_reporters = 'OptimizationReporter/misfit_norm main/misfit_values'
  []

  # ADJOINT transfers
  #NOTE:  the adjoint variable we are transferring is actually the gradient
  [toAdjoint]
    type = MultiAppReporterTransfer
    # We are transferring directly from the forward app to the adjoint app
    to_multi_app = adjoint
    from_reporters = 'main/misfit_values'
    to_reporters = 'misfit/misfit_values'
  []
  [fromAdjoint]
    type = MultiAppReporterTransfer
    from_multi_app = adjoint
    from_reporters = 'gradient/adjoint'
    to_reporters = 'OptimizationReporter/grad_parameter_results'
  []

  # HESSIAN transfers.  Same as forward.
  [toHomoForward]
    type = MultiAppReporterTransfer
    to_multi_app = homogeneousForward
    from_reporters = 'OptimizationReporter/parameter_results'
    to_reporters = 'point_source/value'
  []
  [fromHomoForward]
    type = MultiAppReporterTransfer
    from_multi_app = homogeneousForward
    # Note: We are transferring the simulation values into misfit
    # this has to be done when using general opt and homogenous forward.
    from_reporters = 'measure_data/simulation_values'
    to_reporters = 'main/misfit_values'
  []
[]

[Reporters]
  [optInfo]
    type = OptimizationInfo
  []
[]

[Outputs]
  csv = true
  file_base = main_out
[]

(modules/optimization/test/tests/executioners/basic_optimize/debug_fd.i)

[Optimization]
[]

[OptimizationReporter]
  type = QuadraticMinimize
  parameter_names = 'results'
  num_values = 3
  initial_condition = '5 8 1'
  objective = 0.0
  solution = '1 2 3'
  measurement_points = ''
  measurement_values = ''
[]

[Executioner]
  type = Optimize
  tao_solver = taolmvm
  petsc_options_iname='-tao_fd_gradient -tao_fd_delta -tao_gatol'
  petsc_options_value='true 1e-8 0.1'
  verbose = true
[]

(modules/optimization/test/tests/optimizationreporter/constant_heat_source/main_nonLinear.i)

[Optimization]
[]

[OptimizationReporter]
  type = GeneralOptimization
  objective_name = objective_value
  parameter_names = 'parameter_results'
  num_values = '1'
  initial_condition = '500'
  lower_bounds = '0.1'
  upper_bounds = '10000'
[]

[Reporters]
  [main]
    type = OptimizationData
    measurement_points = '0.2 0.2 0
    0.8 0.6 0
    0.2 1.4 0
    0.8 1.8 0'
    measurement_values = '270 339 321 221'

  []
[]

[Executioner]
  type = Optimize
  tao_solver = taoblmvm
  petsc_options_iname = '-tao_gatol'
  petsc_options_value = '.01'
  verbose = true
[]

[MultiApps]
  [forward]
    type = FullSolveMultiApp
    input_files = forward_nonLinear.i
    execute_on = FORWARD
  []
  [adjoint]
    type = FullSolveMultiApp
    input_files = adjoint_nonLinear.i
    execute_on = ADJOINT
  []
[]

[Transfers]
  [toForward_measument]
    type = MultiAppReporterTransfer
    to_multi_app = forward
    from_reporters = 'main/measurement_xcoord
                      main/measurement_ycoord
                      main/measurement_zcoord
                      main/measurement_time
                      main/measurement_values
                      OptimizationReporter/parameter_results'
    to_reporters = 'measure_data/measurement_xcoord
                    measure_data/measurement_ycoord
                    measure_data/measurement_zcoord
                    measure_data/measurement_time
                    measure_data/measurement_values
                    params/q'
  []
  [toAdjoint]
    type = MultiAppReporterTransfer
    to_multi_app = adjoint
    from_reporters = 'main/measurement_xcoord
                      main/measurement_ycoord
                      main/measurement_zcoord
                      main/measurement_time
                      main/misfit_values
                      OptimizationReporter/parameter_results'
    to_reporters = 'misfit/measurement_xcoord
                    misfit/measurement_ycoord
                    misfit/measurement_zcoord
                    misfit/measurement_time
                    misfit/misfit_values
                    params/q'
  []
  [fromForward]
    type = MultiAppReporterTransfer
    from_multi_app = forward
    from_reporters = 'measure_data/misfit_values measure_data/objective_value'
    to_reporters = 'main/misfit_values OptimizationReporter/objective_value'
  []
  [fromadjoint]
    type = MultiAppReporterTransfer
    from_multi_app = adjoint
    from_reporters = 'gradient_vpp/inner_product'
    to_reporters = 'OptimizationReporter/grad_parameter_results'
  []
  #for temperature dependent material
  [fromforwardMesh]
    type = MultiAppCopyTransfer
    from_multi_app = forward
    to_multi_app = adjoint
    source_variable = 'T'
    variable = 'T'
  []
[]

[Reporters]
  [optInfo]
    type = OptimizationInfo
  []
[]

[Outputs]
  csv = true
[]

(modules/optimization/test/tests/optimizationreporter/bimaterial/main_auto_adjoint.i)

# This main.i file runs the subapps model.i and grad.i, using an FullSolveMultiApp
# The purpose of main.i is to find the two diffusivity_values
# (one in the bottom material of model.i, and one in the top material of model.i)
# such that the misfit between experimental observations (defined in model.i) and MOOSE predictions is minimised.
# The adjoint computed in grad.i is used to compute the gradient for the gradient based LMVM solver in TAO
# PETSc-TAO optimisation is used to perform this inversion
#
[Optimization]
[]

[OptimizationReporter]
  type = GeneralOptimization
  objective_name = objective_value
  parameter_names = diffusivity_values
  num_values = 2 # diffusivity in the bottom material and in the top material of model.i
  initial_condition = '3 4' # the expected result is about '1 10' so this initial condition is not too bad
  lower_bounds = '1'
  upper_bounds = '20'
[]

[Reporters]
  [main]
    type = OptimizationData
    measurement_file = 'synthetic_data.csv'
    file_value = 'temperature'
  []
[]

[Executioner]
  type = Optimize
  tao_solver = taoblmvm
  petsc_options_iname = '-tao_gatol'
  petsc_options_value = '1e-3'
  ## THESE OPTIONS ARE FOR TESTING THE ADJOINT GRADIENT
  # petsc_options_iname='-tao_max_it -tao_fd_test -tao_test_gradient -tao_fd_gradient -tao_fd_delta -tao_gatol'
  # petsc_options_value='1 true true false 1e-8 0.1'
  # petsc_options = '-tao_test_gradient_view'
  verbose = true
[]

[MultiApps]
  [forward]
    type = FullSolveMultiApp
    input_files = model_and_adjoint.i
    execute_on = FORWARD
  []
[]

[Transfers]
  [toForward] #pass the coordinates where we knew the measurements to the forward model to do the extraction of the simulation data at the location of the measurements to compute the misfit
    type = MultiAppReporterTransfer
    to_multi_app = forward
    from_reporters = 'main/measurement_xcoord
                      main/measurement_ycoord
                      main/measurement_zcoord
                      main/measurement_time
                      main/measurement_values
                      OptimizationReporter/diffusivity_values'
    to_reporters = 'measure_data/measurement_xcoord
                    measure_data/measurement_ycoord
                    measure_data/measurement_zcoord
                    measure_data/measurement_time
                    measure_data/measurement_values
                    data/diffusivity'
  []
  [from_forward] #get the simulation values
    type = MultiAppReporterTransfer
    from_multi_app = forward
    from_reporters = 'measure_data/objective_value
                      gradvec/inner_product'
    to_reporters = 'OptimizationReporter/objective_value
                    OptimizationReporter/grad_diffusivity_values'
  []
[]

[Outputs]
  console = true
  csv = true
[]

(modules/optimization/examples/simpleTransient/main_mesh.i)

[Optimization]
[]

[OptimizationReporter]
  type = ParameterMeshOptimization
  objective_name = objective_value
  parameter_names = 'source'
  parameter_meshes = source_mesh_in.e
  num_parameter_times = 11
[]

[Reporters]
  [main]
    type = OptimizationData
  []
[]

[MultiApps]
  [forward]
    type = FullSolveMultiApp
    input_files = forward_mesh.i
    execute_on = FORWARD
  []
  [adjoint]
    type = FullSolveMultiApp
    input_files = adjoint_mesh.i
    execute_on = ADJOINT
  []
[]

[Transfers]
  [to_forward]
    type = MultiAppReporterTransfer
    to_multi_app = forward
    from_reporters = 'OptimizationReporter/source'
    to_reporters = 'src_values/values'
  []
  [from_forward]
    type = MultiAppReporterTransfer
    from_multi_app = forward
    from_reporters = 'measured_data/misfit_values measured_data/objective_value'
    to_reporters = 'main/misfit_values OptimizationReporter/objective_value'
  []
  [to_adjoint]
    type = MultiAppReporterTransfer
    to_multi_app = adjoint
    from_reporters = 'OptimizationReporter/source main/misfit_values'
    to_reporters = 'src_values/values measured_data/misfit_values'
  []
  [from_adjoint]
    type = MultiAppReporterTransfer
    from_multi_app = adjoint
    from_reporters = 'adjoint/inner_product'
    to_reporters = 'OptimizationReporter/grad_source'
  []
[]

[Executioner]
  type = Optimize
  solve_on = none
  tao_solver = taolmvm
  petsc_options_iname = '-tao_gatol -tao_ls_type'
  petsc_options_value = '1e-2 unit'
  verbose = true
[]

(modules/optimization/test/tests/executioners/basic_optimize/debug_gradient.i)

[Optimization]
[]

[OptimizationReporter]
  type = QuadraticMinimize
  parameter_names = 'results'
  num_values = 3
  initial_condition = '5 8 1'
  objective = 0.0
  solution = '1 2 3'
  measurement_points = ''
  measurement_values = ''
[]

[Executioner]
  type = Optimize
  tao_solver = taobncg
  petsc_options_iname='-tao_fd_test -tao_test_gradient -tao_fd_gradient -tao_fd_delta -tao_ls_type'
  petsc_options_value='true true false 1e-8 unit'
  petsc_options = '-tao_test_gradient_view'
  verbose = true
[]

(modules/optimization/test/tests/optimizationreporter/general_opt/point_loads_gen_opt/main_auto_adjoint.i)

[Optimization]
[]

[OptimizationReporter]
  type = GeneralOptimization
  objective_name = misfit_norm
  parameter_names = 'parameter_results'
  num_values = '3'
[]
[Reporters]
  [measure_data]
    type = OptimizationData
    measurement_points = '0.5 0.28 0
                          0.5 0.6 0
                          0.5 0.8 0
                          0.5 1.1 0'
    measurement_values = '293 304 315 320'
  []
[]

[Executioner]
  type = Optimize
  tao_solver = taolmvm
  petsc_options_iname = '-tao_gttol -tao_ls_type'
  petsc_options_value = '1e-5 unit'
  verbose = true
[]

[MultiApps]
  [forward]
    type = FullSolveMultiApp
    input_files = forward_and_adjoint.i
    execute_on = "FORWARD"
  []
[]

[Transfers]
  # FORWARD transfers
  [toForward_measument]
    type = MultiAppReporterTransfer
    to_multi_app = forward
    from_reporters = 'OptimizationReporter/parameter_results'
    to_reporters = 'point_source/value'
  []

  [fromForward]
    type = MultiAppReporterTransfer
    from_multi_app = forward
    from_reporters = 'gradient/temperature_adjoint
                      measure_data/misfit_norm'
    to_reporters = 'OptimizationReporter/grad_parameter_results
                    OptimizationReporter/misfit_norm'
  []
[]

[Outputs]
  csv = true
  file_base = main_out
[]

(modules/optimization/test/tests/optimizationreporter/material/main.i)

[Optimization]
[]

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 10
  ny = 10
  xmax = 2
  ymax = 2
[]

[OptimizationReporter]
  type = GeneralOptimization
  objective_name = objective_value
  parameter_names = 'p1'
  num_values = '1'
  initial_condition = '7'
  lower_bounds = '0'
  upper_bounds = '10'
[]

[Reporters]
  [main]
    type = OptimizationData
    measurement_points = '0.2 0.2 0
              0.8 0.6 0
              0.2 1.4 0
              0.8 1.8 0'
    measurement_values = '226 254 214 146'
  []
[]

[Executioner]
  type = Optimize
  tao_solver = taoblmvm
  petsc_options_iname = '-tao_gatol'
  petsc_options_value = '0.0001'
  verbose = true
[]

[MultiApps]
  [forward]
    type = FullSolveMultiApp
    input_files = forward.i
    execute_on = "FORWARD"
    clone_parent_mesh = true
  []
  [adjoint]
    type = FullSolveMultiApp
    input_files = adjoint.i
    execute_on = "ADJOINT"
    clone_parent_mesh = true
  []
[]

[Transfers]
  [toForward]
    type = MultiAppReporterTransfer
    to_multi_app = forward
    from_reporters = 'main/measurement_xcoord
                      main/measurement_ycoord
                      main/measurement_zcoord
                      main/measurement_time
                      main/measurement_values
                      OptimizationReporter/p1'
    to_reporters = 'measure_data/measurement_xcoord
                    measure_data/measurement_ycoord
                    measure_data/measurement_zcoord
                    measure_data/measurement_time
                    measure_data/measurement_values
                    params/p1'
  []
  [fromForward_mesh]
    type = MultiAppCopyTransfer
    from_multi_app = forward
    to_multi_app = adjoint
    source_variable = 'temperature'
    variable = 'temperature_forward'
  []
  [fromForward]
    type = MultiAppReporterTransfer
    from_multi_app = forward
    from_reporters = 'measure_data/misfit_values measure_data/objective_value'
    to_reporters = 'main/misfit_values OptimizationReporter/objective_value'
  []

  [toAdjoint]
    type = MultiAppReporterTransfer
    to_multi_app = adjoint
    from_reporters = 'main/measurement_xcoord
                      main/measurement_ycoord
                      main/measurement_zcoord
                      main/measurement_time
                      main/misfit_values
                      OptimizationReporter/p1'
    to_reporters = 'misfit/measurement_xcoord
                    misfit/measurement_ycoord
                    misfit/measurement_zcoord
                    misfit/measurement_time
                    misfit/misfit_values
                    params/p1'
  []
  [fromAdjoint]
    type = MultiAppReporterTransfer
    from_multi_app = adjoint
    from_reporters = 'adjoint_grad/inner_product'
    to_reporters = 'OptimizationReporter/grad_p1'
  []
[]

[Outputs]
  csv = true
[]

(modules/optimization/test/tests/outputs/exodus_optimization_steady/main.i)

[Optimization]
[]

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 10
  ny = 10
  xmax = 2
  ymax = 2
[]

[OptimizationReporter]
  type = GeneralOptimization
  objective_name = objective_value
  parameter_names = 'p1'
  num_values = '1'
  initial_condition = '7'
  lower_bounds = '0'
  upper_bounds = '10'
[]

[Reporters]
  [main]
    type = OptimizationData
    measurement_points = '0.2 0.2 0
  0.8 0.6 0
  0.2 1.4 0
  0.8 1.8 0'
    measurement_values = '226 254 214 146'
  []
[]

[Executioner]
  type = Optimize
  tao_solver = taoblmvm
  petsc_options_iname = '-tao_gatol'
  petsc_options_value = '1e-4'
  verbose = true
[]

[MultiApps]
  [forward]
    type = FullSolveMultiApp
    input_files = forward.i
    execute_on = "FORWARD"
    clone_parent_mesh = true
  []
  [adjoint]
    type = FullSolveMultiApp
    input_files = adjoint_iteration_output.i
    execute_on = "ADJOINT"
    clone_parent_mesh = true
  []
[]

[Transfers]
  [toForward]
    type = MultiAppReporterTransfer
    to_multi_app = forward
    from_reporters = 'main/measurement_xcoord
                      main/measurement_ycoord
                      main/measurement_zcoord
                      main/measurement_time
                      main/measurement_values
                      OptimizationReporter/p1'
    to_reporters = 'measure_data/measurement_xcoord
                    measure_data/measurement_ycoord
                    measure_data/measurement_zcoord
                    measure_data/measurement_time
                    measure_data/measurement_values
                    params/p1'
  []
  [fromForward_mesh]
    type = MultiAppCopyTransfer
    from_multi_app = forward
    to_multi_app = adjoint
    source_variable = 'temperature'
    variable = 'temperature_forward'
  []
  [fromForward]
    type = MultiAppReporterTransfer
    from_multi_app = forward
    from_reporters = 'measure_data/misfit_values measure_data/objective_value'
    to_reporters = 'main/misfit_values OptimizationReporter/objective_value'
  []

  [toAdjoint]
    type = MultiAppReporterTransfer
    to_multi_app = adjoint
    from_reporters = 'main/measurement_xcoord
                      main/measurement_ycoord
                      main/measurement_zcoord
                      main/measurement_time
                      main/misfit_values
                      OptimizationReporter/p1'
    to_reporters = 'misfit/measurement_xcoord
                    misfit/measurement_ycoord
                    misfit/measurement_zcoord
                    misfit/measurement_time
                    misfit/misfit_values
                    params/p1'
  []
  [fromAdjoint]
    type = MultiAppReporterTransfer
    from_multi_app = adjoint
    from_reporters = 'adjoint_grad/inner_product'
    to_reporters = 'OptimizationReporter/grad_p1'
  []
[]

[Outputs]
  csv = true
[]

(modules/optimization/test/tests/executioners/constrained/inequality/main_auto_adjoint.i)

# This tests constrained optimization of a linear and constant function
# that are used to apply NuemannBCs on a side.

[Optimization]
[]

[OptimizationReporter]
  type = GeneralOptimization
  objective_name = objective_value
  parameter_names = 'left'
  num_values = '2'
  initial_condition = '10 10'
  lower_bounds = '0'
  upper_bounds = '1000'

  inequality_names = 'ineq'

[]
[Reporters]
  [main]
    type = OptimizationData
    measurement_points = '0.2 0.2 0'
    measurement_values = '207'
    file_value = 'measured_value'
  []
[]

[Executioner]
  type = Optimize
  tao_solver = taoalmm
  petsc_options_iname = '-tao_gatol -tao_catol  -tao_almm_type -tao_almm_mu_factor -tao_almm_mu_init  -tao_almm_subsolver_tao_type'
  petsc_options_value = ' 1e-3 1e-3  phr  1.1 1.0 bqnktr'
  verbose = true
[]

[MultiApps]
  [forward]
    type = FullSolveMultiApp
    input_files = forward_and_adjoint.i
    execute_on = "FORWARD"
  []
[]
[Reporters]
  [optInfo]
    type = OptimizationInfo
  []
[]

[Transfers]
  [toForward]
    type = MultiAppReporterTransfer
    to_multi_app = forward
    from_reporters = 'main/measurement_xcoord
                      main/measurement_ycoord
                      main/measurement_zcoord
                      main/measurement_time
                      main/measurement_values
                      OptimizationReporter/left'
    to_reporters = 'measure_data/measurement_xcoord
                    measure_data/measurement_ycoord
                    measure_data/measurement_zcoord
                    measure_data/measurement_time
                    measure_data/measurement_values
                    params/left'
  []
  [fromForward]
    type = MultiAppReporterTransfer
    from_multi_app = forward
    from_reporters = 'measure_data/objective_value
                      grad_bc_left/inner_product
                      ineq/ineq
                      gradient_c/gradient_c'
    to_reporters = 'OptimizationReporter/objective_value
                    OptimizationReporter/grad_left
                    OptimizationReporter/ineq
                    OptimizationReporter/grad_ineq'
  []
[]

(modules/optimization/test/tests/optimizationreporter/mesh_source/main_auto_adjoint.i)

[Optimization]
[]

[OptimizationReporter]
  type = ParameterMeshOptimization
  objective_name = objective_value
  parameter_names = 'source'
  parameter_meshes = 'parameter_mesh_in.e'
[]
[Reporters]
  [main]
    type = OptimizationData
    # Random points
    measurement_points = '0.78193073 0.39115321 0
  0.72531893 0.14319403 0
  0.14052488 0.86976625 0
  0.401893   0.54241797 0
  0.02645427 0.43320192 0
  0.28856889 0.0035165  0
  0.51433644 0.94485949 0
  0.29252255 0.7962032  0
  0.04925654 0.58018889 0
  0.04717357 0.9556314  0'
    # sin(x*pi/2)*sin(y*pi/2)
    measurement_values = '0.54299466 0.20259611 0.21438235 0.44418597 0.02613676
  0.00241892 0.72014019 0.42096307 0.06108895 0.07385256'
  []
[]

[Executioner]
  type = Optimize
  tao_solver = taobqnls
  petsc_options_iname = '-tao_gatol'
  petsc_options_value = '1e-4'
  verbose = true
[]

[MultiApps]
  [forward]
    type = FullSolveMultiApp
    input_files = forward_and_adjoint.i
    execute_on = FORWARD
  []
[]

[Transfers]
  [toForward_measument]
    type = MultiAppReporterTransfer
    to_multi_app = forward
    from_reporters = 'main/measurement_xcoord
                      main/measurement_ycoord
                      main/measurement_zcoord
                      main/measurement_time
                      main/measurement_values
                      OptimizationReporter/source'
    to_reporters = 'measure_data/measurement_xcoord
                    measure_data/measurement_ycoord
                    measure_data/measurement_zcoord
                    measure_data/measurement_time
                    measure_data/measurement_values
                    src_rep/vals'
  []
  [fromForward]
    type = MultiAppReporterTransfer
    from_multi_app = forward
    from_reporters = 'measure_data/objective_value
                      gradient_vpp/inner_product'
    to_reporters = 'OptimizationReporter/objective_value
                    OptimizationReporter/grad_source'
  []
[]

(modules/optimization/examples/materialTransient/optimize_auto_adjoint.i)

[Optimization]
[]

[OptimizationReporter]
  type = GeneralOptimization
  objective_name = objective_value
  parameter_names = 'D'
  num_values = '4'
  initial_condition = '0.01 0.01 0.01 0.01'
  upper_bounds = '1e2'
  lower_bounds = '1e-3'
[]

[Reporters]
  [main]
    type = OptimizationData

    measurement_file = forward_out_data_0011.csv
    file_xcoord = measurement_xcoord
    file_ycoord = measurement_ycoord
    file_zcoord = measurement_zcoord
    file_time = measurement_time
    file_value = simulation_values
  []
[]

[MultiApps]
  [forward]
    type = FullSolveMultiApp
    input_files = forward_and_adjoint.i
    execute_on = FORWARD
  []
[]

[Transfers]
  [to_forward]
    type = MultiAppReporterTransfer
    to_multi_app = forward
    from_reporters = 'main/measurement_xcoord
                      main/measurement_ycoord
                      main/measurement_zcoord
                      main/measurement_time
                      main/measurement_values
                      OptimizationReporter/D'
    to_reporters = 'data/measurement_xcoord
                    data/measurement_ycoord
                    data/measurement_zcoord
                    data/measurement_time
                    data/measurement_values
                    diffc_rep/D_vals'
  []
  [from_forward]
    type = MultiAppReporterTransfer
    from_multi_app = forward
    from_reporters = 'data/objective_value
                      adjoint/inner_product'
    to_reporters = 'OptimizationReporter/objective_value
                    OptimizationReporter/grad_D'
  []
[]

[Executioner]
  type = Optimize
  tao_solver = taobqnls
  petsc_options_iname = '-tao_gatol'
  petsc_options_value = '1e-4'
[]

(modules/optimization/test/tests/optimizationreporter/point_loads/main.i)

# DO NOT CHANGE THIS TEST
# this test is documented as an example in forceInv_pointLoads.md
# if this test is changed, the figures will need to be updated.
measurement_points = '0.5 0.28 0
   0.5 0.6 0
   0.5 0.8 0
   0.5 1.1 0'
measurement_values = '293 304 315 320'
[Optimization]
[]

[OptimizationReporter]
  type = GeneralOptimization
  objective_name = objective_value
  parameter_names = 'parameter_results'
  num_values = '3'
[]

[Reporters]
  [main]
    type = OptimizationData
    measurement_points = ${measurement_points}
    measurement_values = ${measurement_values}
  []
[]

[Executioner]
  type = Optimize
  tao_solver = taonls
  petsc_options_iname = '-tao_gttol -tao_max_it -tao_nls_pc_type -tao_nls_ksp_type'
  petsc_options_value = '1e-5 10 none cg'
  verbose = true
[]

[MultiApps]
  [forward]
    type = FullSolveMultiApp
    input_files = forward.i
    execute_on = "FORWARD"
  []
  [adjoint]
    type = FullSolveMultiApp
    input_files = adjoint.i
    execute_on = "ADJOINT"
  []
  [homogeneousForward]
    type = FullSolveMultiApp
    input_files = forward_homogeneous.i
    execute_on = "HOMOGENEOUS_FORWARD"
  []
[]

[Transfers]
  # FORWARD transfers
  [toForward_measument]
    type = MultiAppReporterTransfer
    to_multi_app = forward
    from_reporters = 'main/measurement_xcoord
                      main/measurement_ycoord
                      main/measurement_zcoord
                      main/measurement_time
                      main/measurement_values
                      OptimizationReporter/parameter_results'
    to_reporters = 'measure_data/measurement_xcoord
                    measure_data/measurement_ycoord
                    measure_data/measurement_zcoord
                    measure_data/measurement_time
                    measure_data/measurement_values
                    point_source/value'
  []
  [fromForward]
    type = MultiAppReporterTransfer
    from_multi_app = forward
    # Note: We are transferring the misfit values into main misfit
    from_reporters = 'measure_data/objective_value measure_data/misfit_values'
    to_reporters = 'OptimizationReporter/objective_value main/misfit_values'
  []

  # ADJOINT transfers
  #NOTE:  the adjoint variable we are transferring is actually the gradient
  [toAdjoint]
    type = MultiAppReporterTransfer
    to_multi_app = adjoint
    from_reporters = 'main/measurement_xcoord
                      main/measurement_ycoord
                      main/measurement_zcoord
                      main/measurement_time
                      main/misfit_values'
    to_reporters = 'misfit/measurement_xcoord
                    misfit/measurement_ycoord
                    misfit/measurement_zcoord
                    misfit/measurement_time
                    misfit/misfit_values'
  []
  [fromAdjoint]
    type = MultiAppReporterTransfer
    from_multi_app = adjoint
    from_reporters = 'gradient/adjoint'
    to_reporters = 'OptimizationReporter/grad_parameter_results'
  []

  # HESSIAN transfers.  Same as forward.
  [toHomoForward]
    type = MultiAppReporterTransfer
    multi_app = homogeneousForward
    direction = to_multiapp
    from_reporters = 'main/measurement_xcoord
                      main/measurement_ycoord
                      main/measurement_zcoord
                      main/measurement_time
                      main/measurement_values
                      OptimizationReporter/parameter_results'
    to_reporters = 'measure_data/measurement_xcoord
                    measure_data/measurement_ycoord
                    measure_data/measurement_zcoord
                    measure_data/measurement_time
                    measure_data/measurement_values
                    point_source/value'
  []
  [fromHomoForward]
    type = MultiAppReporterTransfer
    multi_app = homogeneousForward
    direction = from_multiapp
    # Note: We are transferring the simulation values into misfit
    # this has to be done when using general opt and homogenous forward.
    from_reporters = 'measure_data/simulation_values'
    to_reporters = 'main/misfit_values'
  []
[]

[Reporters]
  [optInfo]
    type = OptimizationInfo
  []
[]

[Outputs]
  csv = true
[]

(modules/optimization/test/tests/optimizationreporter/nonlinear_material/main.i)

[Optimization]
[]

[OptimizationReporter]
  type = GeneralOptimization
  objective_name = objective_value
  parameter_names = 'heat_source'
  num_values = '1'
  initial_condition = '0'
  lower_bounds = '0.1'
  upper_bounds = '10000'
[]

[Reporters]
  [main]
    type = OptimizationData
    measurement_points = '0.2 0.2 0
                          0.8 0.6 0
                          0.2 1.4 0
                          0.8 1.8 0'
    measurement_values = '1.98404 1.91076 1.56488 1.23863'
  []
[]

[Executioner]
  type = Optimize
  tao_solver = taolmvm
  petsc_options_iname = '-tao_gttol'
  petsc_options_value = ' 1e-5'
  verbose = true
[]

[MultiApps]
  [forward]
    type = FullSolveMultiApp
    input_files = forward_and_adjoint.i
    execute_on = FORWARD
  []
[]

[Transfers]
  [to_forward]
    type = MultiAppReporterTransfer
    to_multi_app = forward
    from_reporters = 'main/measurement_xcoord
                      main/measurement_ycoord
                      main/measurement_zcoord
                      main/measurement_time
                      main/measurement_values
                      OptimizationReporter/heat_source'
    to_reporters = 'measurement_locations/measurement_xcoord
                    measurement_locations/measurement_ycoord
                    measurement_locations/measurement_zcoord
                    measurement_locations/measurement_time
                    measurement_locations/measurement_values
                    params/heat_source'
  []
  [from_forward]
    type = MultiAppReporterTransfer
    from_multi_app = forward
    from_reporters = 'measurement_locations/objective_value
                      gradient_vpp/inner_product'
    to_reporters = 'OptimizationReporter/objective_value
                    OptimizationReporter/grad_heat_source'
  []
[]

[Outputs]
  csv = true
[]

(modules/optimization/examples/materialTransient/optimize_grad.i)

[Optimization]
[]

[OptimizationReporter]
  type = GeneralOptimization
  objective_name = objective_value
  parameter_names = 'D'
  num_values = '4'
  initial_condition = '0.01 0.01 0.01 0.01'
  upper_bounds = '1e2'
  lower_bounds = '1e-3'
[]

[Reporters]
  [main]
    type = OptimizationData

    measurement_file = forward_out_data_0011.csv
    file_xcoord = measurement_xcoord
    file_ycoord = measurement_ycoord
    file_zcoord = measurement_zcoord
    file_time = measurement_time
    file_value = simulation_values
  []
[]

[MultiApps]
  [forward]
    type = FullSolveMultiApp
    input_files = forward.i
    cli_args = 'Outputs/csv=false;Outputs/console=false'
    execute_on = FORWARD
  []
  [adjoint]
    type = FullSolveMultiApp
    input_files = gradient.i
    cli_args = 'Outputs/console=false;UserObjects/load_u/mesh=optimize_grad_out_forward0.e'
    execute_on = ADJOINT
  []
[]

[Transfers]
  [to_forward]
    type = MultiAppReporterTransfer
    to_multi_app = forward
    from_reporters = 'main/measurement_xcoord
                      main/measurement_ycoord
                      main/measurement_zcoord
                      main/measurement_time
                      main/measurement_values
                      OptimizationReporter/D'
    to_reporters = 'data/measurement_xcoord
                    data/measurement_ycoord
                    data/measurement_zcoord
                    data/measurement_time
                    data/measurement_values
                    diffc_rep/D_vals'
  []
  [from_forward]
    type = MultiAppReporterTransfer
    from_multi_app = forward
    from_reporters = 'data/misfit_values data/objective_value'
    to_reporters = 'main/misfit_values OptimizationReporter/objective_value'
  []
  [to_adjoint]
    type = MultiAppReporterTransfer
    to_multi_app = adjoint
    from_reporters = 'main/measurement_xcoord
                      main/measurement_ycoord
                      main/measurement_zcoord
                      main/measurement_time
                      main/misfit_values
                      OptimizationReporter/D'
    to_reporters = 'data/measurement_xcoord
                    data/measurement_ycoord
                    data/measurement_zcoord
                    data/measurement_time
                    data/misfit_values
                    diffc_rep/D_vals'
  []
  [from_adjoint]
    type = MultiAppReporterTransfer
    from_multi_app = adjoint
    from_reporters = 'adjoint/inner_product'
    to_reporters = 'OptimizationReporter/grad_D'
  []
[]

[Executioner]
  type = Optimize
  tao_solver = taobqnls
  petsc_options_iname = '-tao_gatol'
  petsc_options_value = '1e-4'
[]

(modules/optimization/test/tests/optimizationreporter/general_opt/function_optimization/main.i)

[Optimization]
[]

[OptimizationReporter]
  type = GeneralOptimization
  parameter_names = 'vals'
  num_values = '2'
  objective_name = obj_value
[]

[Problem]
  solve = false
[]
[Executioner]
  type = Optimize
  tao_solver = taobqnktr
  petsc_options_iname = '-tao_gatol'
  petsc_options_value = '1e-8 '
  verbose = true
  output_optimization_iterations = true
[]

[MultiApps]
  [forward]
    type = FullSolveMultiApp
    input_files = forward.i
    execute_on = FORWARD
  []
[]

[Transfers]
  [toForward]
    type = MultiAppReporterTransfer
    to_multi_app = forward
    from_reporters = 'OptimizationReporter/vals'
    to_reporters = 'vals/vals'
  []

  [fromForward]
    type = MultiAppReporterTransfer
    from_multi_app = forward
    from_reporters = 'obj_pp/value
                      grad_f/grad_f'
    to_reporters = 'OptimizationReporter/obj_value
                    OptimizationReporter/grad_vals'
  []
[]

[Outputs]
  [json]
    type = JSON
    execute_system_information_on = none
  []
  [json_forward]
    type = JSON
    execute_on = 'FORWARD '
    execute_system_information_on = none
  []
[]

(modules/optimization/test/tests/optimizationreporter/mesh_source/main_linearRestart.i)

[Optimization]
[]

[OptimizationReporter]
  type = ParameterMeshOptimization
  objective_name = objective_value
  parameter_names = 'source'
  parameter_meshes = 'parameter_mesh_restart_out.e'
  exodus_timesteps_for_parameter_mesh_variable = 2
  initial_condition_mesh_variable = restart_source
  lower_bounds = -1
  upper_bounds = 5
  outputs = none
[]

[Reporters]
  [main]
    type = OptimizationData
    # Random points
    measurement_points = '0.78193073 0.39115321 0
  0.72531893 0.14319403 0
  0.14052488 0.86976625 0
  0.401893   0.54241797 0
  0.02645427 0.43320192 0
  0.28856889 0.0035165  0
  0.51433644 0.94485949 0
  0.29252255 0.7962032  0
  0.04925654 0.58018889 0
  0.04717357 0.9556314  0'
    # sin(x*pi/2)*sin(y*pi/2)
    measurement_values = '0.54299466 0.20259611 0.21438235 0.44418597 0.02613676
  0.00241892 0.72014019 0.42096307 0.06108895 0.07385256'
  []
[]

[Executioner]
  type = Optimize
  tao_solver = taoblmvm
  petsc_options_iname = '-tao_gatol'
  petsc_options_value = '1e-4'
  verbose = true
[]

[MultiApps]
  [forward]
    type = FullSolveMultiApp
    input_files = forward.i
    execute_on = FORWARD
  []
  [adjoint]
    type = FullSolveMultiApp
    input_files = adjoint.i
    execute_on = ADJOINT
  []
[]

[Transfers]
  [toForward_measument]
    type = MultiAppReporterTransfer
    to_multi_app = forward
    from_reporters = 'main/measurement_xcoord
                      main/measurement_ycoord
                      main/measurement_zcoord
                      main/measurement_time
                      main/measurement_values
                      OptimizationReporter/source'
    to_reporters = 'measure_data/measurement_xcoord
                    measure_data/measurement_ycoord
                    measure_data/measurement_zcoord
                    measure_data/measurement_time
                    measure_data/measurement_values
                    src_rep/vals'
  []
  [toAdjoint]
    type = MultiAppReporterTransfer
    to_multi_app = adjoint
    from_reporters = 'main/measurement_xcoord
                      main/measurement_ycoord
                      main/measurement_zcoord
                      main/measurement_time
                      main/misfit_values
                      OptimizationReporter/source'
    to_reporters = 'misfit/measurement_xcoord
                    misfit/measurement_ycoord
                    misfit/measurement_zcoord
                    misfit/measurement_time
                    misfit/misfit_values
                    src_rep/vals'
  []
  [fromForward]
    type = MultiAppReporterTransfer
    from_multi_app = forward
    from_reporters = 'measure_data/misfit_values measure_data/objective_value'
    to_reporters = 'main/misfit_values OptimizationReporter/objective_value'
  []
  [fromadjoint]
    type = MultiAppReporterTransfer
    from_multi_app = adjoint
    from_reporters = 'gradient_vpp/inner_product'
    to_reporters = 'OptimizationReporter/grad_source'
  []
[]

[Reporters]
  [optInfo]
    type = OptimizationInfo
    items = 'current_iterate function_value gnorm'
  []
[]

[Outputs]
  csv = true
[]

(modules/optimization/examples/simpleTransient/main_auto_adjoint.i)

[Optimization]
[]

[OptimizationReporter]
  type = GeneralOptimization
  objective_name = objective_value
  parameter_names = 'source'
  num_values = '44'
[]

[MultiApps]
  [forward]
    type = FullSolveMultiApp
    input_files = forward_and_adjoint.i
    execute_on = FORWARD
  []
[]

[Transfers]
  [to_forward]
    type = MultiAppReporterTransfer
    to_multi_app = forward
    from_reporters = 'OptimizationReporter/source'
    to_reporters = 'src_values/values'
  []
  [from_forward]
    type = MultiAppReporterTransfer
    from_multi_app = forward
    from_reporters = 'measured_data/objective_value adjoint/inner_product'
    to_reporters = 'OptimizationReporter/objective_value OptimizationReporter/grad_source'
  []
[]

[Executioner]
  type = Optimize
  solve_on = none
  tao_solver = taolmvm
  petsc_options_iname = '-tao_gatol -tao_ls_type'
  petsc_options_value = '1e-2 unit'
  verbose = true
[]

(modules/optimization/test/tests/executioners/constrained/equality/quadratic_minimize_constrained.i)

[Optimization]
[]

[OptimizationReporter]
  type = QuadraticMinimizeConstrained
  parameter_names = 'results'
  num_values = 3
  initial_condition = '1 1 1'
  objective = 0.0
  solution = '1 2 3'
  solution_sum_equality = 5.0
  measurement_points = ''
  measurement_values = ''
  equality_names = 'equal'

[]

[Executioner]
  type = Optimize
  tao_solver = taoalmm
  solve_on = none
  verbose = true
  petsc_options_iname = '-tao_gttol -tao_catol  -tao_almm_type -tao_almm_mu_factor '
  petsc_options_value = ' 3e-5 1e-4  phr  1.1'

[]

[Outputs]
  csv = true
[]

(modules/optimization/examples/diffusion_reaction/optimize.i)

[Optimization]
[]

[OptimizationReporter]
  type = ParameterMeshOptimization
  objective_name = objective_value
  parameter_names = 'reaction_rate'
  parameter_meshes = 'parameter_mesh_out.e'

  initial_condition = 0
  lower_bounds = 0

[]

[Reporters]
  [main]
    type = OptimizationData
    measurement_file = forward_exact_csv_sample_0011.csv
    file_xcoord = measurement_xcoord
    file_ycoord = measurement_ycoord
    file_zcoord = measurement_zcoord
    file_time = measurement_time
    file_value = simulation_values
  []
[]

[MultiApps]
  [forward]
    type = FullSolveMultiApp
    input_files = forward_and_adjoint.i
    execute_on = FORWARD
  []
[]

[Transfers]
  [to_forward]
    type = MultiAppReporterTransfer
    to_multi_app = forward
    from_reporters = 'main/measurement_xcoord
                      main/measurement_ycoord
                      main/measurement_zcoord
                      main/measurement_time
                      main/measurement_values
                      OptimizationReporter/reaction_rate'
    to_reporters = 'data/measurement_xcoord
                    data/measurement_ycoord
                    data/measurement_zcoord
                    data/measurement_time
                    data/measurement_values
                    params/reaction_rate'
  []
  [from_forward]
    type = MultiAppReporterTransfer
    from_multi_app = forward
    from_reporters = 'adjoint/inner_product data/objective_value'
    to_reporters = 'OptimizationReporter/grad_reaction_rate OptimizationReporter/objective_value'
  []
[]

[Reporters]
  [optInfo]
    type = OptimizationInfo
    items = 'current_iterate function_value gnorm'
  []
[]

[Executioner]
  type = Optimize
  tao_solver = taobqnls
  petsc_options_iname = '-tao_gttol -tao_max_it'
  #petsc_options_value = '1e-5 100' #use this to get results for paper
  petsc_options_value = '1e-5 5'
  solve_on = 'NONE'
  verbose = true
[]
[Outputs]
  csv = true
[]

(modules/optimization/test/tests/executioners/basic_optimize/qm_multi_param.i)

[Optimization]
[]

[OptimizationReporter]
  type = QuadraticMinimize
  parameter_names = 'result1 result2 result3'
  num_values = '3 2 2'
  initial_condition = '5 4 2; 9 5; 1 0'
  objective = 1.0
  solution = '1 2 3 4 5 6 7'
  measurement_points = ''
  measurement_values = ''
[]

[Executioner]
  type = Optimize
  tao_solver = TAOBNCG
  petsc_options_iname = '-tao_gatol -tao_cg_delta_max'
  petsc_options_value = '1e-4 1e-2'
  solve_on = none
  verbose = true
[]

[Outputs]
  csv = true
[]

(modules/combined/test/tests/optimization/invOpt_bc_convective/main.i)

[Optimization]
[]

[Mesh]
  [gmg]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 10
    ny = 20
    xmax = 1
    ymax = 2
  []
[]

[OptimizationReporter]
  type = GeneralOptimization
  objective_name = objective_value
  parameter_names = 'p1'
  num_values = '1'
  initial_condition = '9'
  upper_bounds = '10'
  lower_bounds = '1'
[]

[Reporters]
  [main]
    type = OptimizationData
    measurement_points = '0.1  0  0
                        0.1  0.1  0
                        0.1  0.2  0
                        0.1  0.3  0
                        0.1  0.4  0
                        0.1  0.5  0
                        0.1  0.6  0
                        0.1  0.7  0
                        0.1  0.8  0
                        0.1  0.9  0
                        0.1  1  0
                        0.1  1.1  0
                        0.1  1.2  0
                        0.1  1.3  0
                        0.1  1.4  0
                        0.1  1.5  0
                        0.1  1.6  0
                        0.1  1.7  0
                        0.1  1.8  0
                        0.1  1.9  0
                        0.1  2    0'
    measurement_values = '500
                        472.9398111
                        450.8117197
                        434.9560747
                        423.3061045
                        414.9454912
                        409.3219399
                        406.1027006
                        405.0865428
                        406.1604905
                        409.2772668
                        414.4449772
                        421.7253934
                        431.2401042
                        443.1862012
                        457.8664824
                        475.7450186
                        497.5582912
                        524.4966003
                        559.1876637
                        600'
  []
[]

[Executioner]
  type = Optimize
  tao_solver = taoblmvm #taolmvm#taonm #taolmvm
  petsc_options_iname = '-tao_gatol' # -tao_fd_gradient -tao_fd_delta'
  petsc_options_value = '1e-4' #1e-1 '#true 1e-4'
[]

[MultiApps]
  [forward]
    type = FullSolveMultiApp
    input_files = forward.i
    execute_on = "FORWARD"
    clone_parent_mesh = true
  []
  [adjoint]
    type = FullSolveMultiApp
    input_files = adjoint.i
    execute_on = "ADJOINT"
    clone_parent_mesh = true
  []
[]

[Transfers]
  #these are usually the same for all input files.
  [toForward]
    type = MultiAppReporterTransfer
    to_multi_app = forward
    from_reporters = 'main/measurement_xcoord
                      main/measurement_ycoord
                      main/measurement_zcoord
                      main/measurement_time
                      main/measurement_values
                      OptimizationReporter/p1'
    to_reporters = 'measure_data/measurement_xcoord
                    measure_data/measurement_ycoord
                    measure_data/measurement_zcoord
                    measure_data/measurement_time
                    measure_data/measurement_values
                    params/vals'
  []
  [fromForward]
    type = MultiAppReporterTransfer
    from_multi_app = forward
    from_reporters = 'measure_data/misfit_values measure_data/objective_value'
    to_reporters = 'main/misfit_values OptimizationReporter/objective_value'
  []
  [toAdjoint]
    type = MultiAppReporterTransfer
    to_multi_app = adjoint
    from_reporters = 'main/measurement_xcoord
                      main/measurement_ycoord
                      main/measurement_zcoord
                      main/measurement_time
                      main/misfit_values
                      OptimizationReporter/p1'
    to_reporters = 'misfit/measurement_xcoord
                    misfit/measurement_ycoord
                    misfit/measurement_zcoord
                    misfit/measurement_time
                    misfit/misfit_values
                    params/vals'
  []
  [fromAdjoint]
    type = MultiAppReporterTransfer
    from_multi_app = adjoint
    from_reporters = 'adjoint_pt/inner_product'
    to_reporters = 'OptimizationReporter/grad_p1'
  []

  # these are transferring data from subapp to subapp because the adjoint problem
  # needs the forward solution to compute the gradient.  Maybe this step could be
  # done on the main app.  The adjoint only passes the adjoint variable (whole mesh)
  # to the main app and the main app computes the gradient from this.
  [fromForwardtoAdjoint_temp]
    type = MultiAppCopyTransfer
    from_multi_app = forward
    to_multi_app = adjoint
    source_variable = 'temperature'
    variable = 'temperature_forward'
  []
[]

[Outputs]
  csv = true
[]

(modules/optimization/test/tests/executioners/basic_optimize/quadratic_minimize.i)

[Optimization]
[]

[OptimizationReporter]
  type = QuadraticMinimize
  parameter_names = 'results'
  num_values = 3
  initial_condition = '5 8 1'
  objective = 0.0
  solution = '1 2 3'
  measurement_points = ''
  measurement_values = ''
[]

[Executioner]
  type = Optimize
  tao_solver = taobncg
  solve_on = none
  verbose = true
[]

[Outputs]
  csv = true
[]

(modules/optimization/test/tests/optimizationreporter/bimaterial/main.i)

# This main.i file runs the subapps model.i and grad.i, using an FullSolveMultiApp
# The purpose of main.i is to find the two diffusivity_values
# (one in the bottom material of model.i, and one in the top material of model.i)
# such that the misfit between experimental observations (defined in model.i) and MOOSE predictions is minimised.
# The adjoint computed in grad.i is used to compute the gradient for the gradient based LMVM solver in TAO
# PETSc-TAO optimisation is used to perform this inversion
#
[Optimization]
[]

[Mesh]
  [gmg]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 16
    ny = 16
    xmin = -4
    xmax = 4
    ymin = -4
    ymax = 4
  []
[]

[OptimizationReporter]
  type = GeneralOptimization
  objective_name = objective_value
  parameter_names = diffusivity_values
  num_values = 2 # diffusivity in the bottom material and in the top material of model.i
  initial_condition = '15 15' # the expected result is about '1 10' so this initial condition is not too bad
  lower_bounds = '1'
  upper_bounds = '50'
[]

[Reporters]
  [main]
    type = OptimizationData
    measurement_file = 'synthetic_data.csv'
    file_value = 'temperature'
  []
[]

[Executioner]
  # type = Optimize
  # tao_solver = taoblmvm
  # petsc_options_iname = '-tao_fd_gradient -tao_gatol'
  # petsc_options_value = ' true            0.001'
  type = Optimize
  tao_solver = taobqnktr
  petsc_options_iname = '-tao_gatol'
  petsc_options_value = '1e-3'
  ## THESE OPTIONS ARE FOR TESTING THE ADJOINT GRADIENT
  # petsc_options_iname='-tao_max_it -tao_fd_test -tao_test_gradient -tao_fd_gradient -tao_fd_delta -tao_gatol'
  # petsc_options_value='1 true true false 1e-8 0.1'
  # petsc_options = '-tao_test_gradient_view'
  verbose = true
[]

[MultiApps]
  [forward]
    type = FullSolveMultiApp
    input_files = model.i
    execute_on = FORWARD
  []
  [adjoint]
    type = FullSolveMultiApp
    input_files = grad.i #write this input file to compute the adjoint solution and the gradient
    execute_on = ADJOINT
  []
[]

[Transfers]
  [toForward] #pass the coordinates where we knew the measurements to the forward model to do the extraction of the simulation data at the location of the measurements to compute the misfit
    type = MultiAppReporterTransfer
    to_multi_app = forward
    from_reporters = 'main/measurement_xcoord
                      main/measurement_ycoord
                      main/measurement_zcoord
                      main/measurement_time
                      main/measurement_values
                      OptimizationReporter/diffusivity_values'
    to_reporters = 'measure_data/measurement_xcoord
                    measure_data/measurement_ycoord
                    measure_data/measurement_zcoord
                    measure_data/measurement_time
                    measure_data/measurement_values
                    data/diffusivity'
  []
  [from_forward] #get the simulation values
    type = MultiAppReporterTransfer
    from_multi_app = forward
    from_reporters = 'measure_data/misfit_values measure_data/objective_value'
    to_reporters = 'main/misfit_values OptimizationReporter/objective_value'
  []
  #############
  #copy the temperature variable - we will need this for the computation of the gradient
  [fromforwardMesh]
    type = MultiAppCopyTransfer
    from_multi_app = forward
    to_multi_app = adjoint
    source_variable = 'temperature'
    variable = 'temperature_forward'
  []
  #############
  [toAdjoint] #pass the misfit to the adjoint
    type = MultiAppReporterTransfer
    to_multi_app = adjoint
    from_reporters = 'main/measurement_xcoord
                      main/measurement_ycoord
                      main/measurement_zcoord
                      main/measurement_time
                      main/misfit_values
                      OptimizationReporter/diffusivity_values'
    to_reporters = 'misfit/measurement_xcoord
                    misfit/measurement_ycoord
                    misfit/measurement_zcoord
                    misfit/measurement_time
                    misfit/misfit_values
                    data/diffusivity'
  []
  [fromadjoint]
    type = MultiAppReporterTransfer
    from_multi_app = adjoint
    from_reporters = 'gradvec/inner_product'
    to_reporters = 'OptimizationReporter/grad_diffusivity_values'
  []
[]

[Outputs]
  console = false
  csv = true
[]

(modules/optimization/examples/materialFrequency/wave1D/inversion.i)

[Optimization]
[]
[OptimizationReporter]
  type = GeneralOptimization
  parameter_names = 'G'
  num_values = 1
  # Converges when initital value is in between 3.99 and 4.01, e.g. 3.95 and 4.05 diverge
  initial_condition = '3.98'
  lower_bounds = '1'
  upper_bounds = '10'
  objective_name = objective
[]
[Executioner]
  type = Optimize
  tao_solver = taoblmvm
  petsc_options_iname = '-tao_gatol -tao_max_it -tao_ls_type'
  petsc_options_value = '1e-8 100 unit'
  verbose = true
[]
[Reporters]
  [OptimizationInfo]
    type = OptimizationInfo
    items = 'current_iterate function_value gnorm'
  []
[]
[Outputs]
  csv = true
[]
[MultiApps]
  [model_grad_sampler]
    type = FullSolveMultiApp
    input_files = 'sampler.i'
    execute_on = FORWARD
  []
[]
[Transfers]
  [SetParameters]
    type = MultiAppReporterTransfer
    to_multi_app = model_grad_sampler
    from_reporters = 'OptimizationReporter/G'
    to_reporters = 'parameters/G'
  []
  [GetObjectiveGradient]
    type = MultiAppReporterTransfer
    from_multi_app = model_grad_sampler
    from_reporters = 'objective/objective
                      gradient/gradient'
    to_reporters = 'OptimizationReporter/objective
                    OptimizationReporter/grad_G'
  []
[]

(modules/optimization/examples/materialTransient/optimize_nograd.i)

[Optimization]
[]

[OptimizationReporter]
  type = GeneralOptimization
  objective_name = objective_value
  parameter_names = 'D'
  num_values = '4'
  initial_condition = '0.2 0.2 0.2 0.2'
[]

[Reporters]
  [main]
    type = OptimizationData

    measurement_file = forward_out_data_0011.csv
    file_xcoord = measurement_xcoord
    file_ycoord = measurement_ycoord
    file_zcoord = measurement_zcoord
    file_time = measurement_time
    file_value = simulation_values
  []
[]

[MultiApps]
  [forward]
    type = FullSolveMultiApp
    input_files = forward.i
    cli_args = 'Outputs/csv=false;Outputs/console=false'
    execute_on = FORWARD
  []
[]

[Transfers]
  [to_forward]
    type = MultiAppReporterTransfer
    to_multi_app = forward
    from_reporters = 'main/measurement_values
                      OptimizationReporter/D'
    to_reporters = 'data/measurement_values
                    diffc_rep/D_vals'
  []
  [from_forward]
    type = MultiAppReporterTransfer
    from_multi_app = forward
    from_reporters = 'data/objective_value'
    to_reporters = 'OptimizationReporter/objective_value'
  []
[]

[Executioner]
  type = Optimize
  tao_solver = taonm
  petsc_options_iname = '-tao_gatol -tao_nm_lambda'
  petsc_options_value = '1e-8 0.25'
  verbose = true
[]

(modules/optimization/test/tests/optimizationreporter/bc_load_linearFunction/main.i)

# This tests that a linear and constant function can be scaled in
# two separate functionNeumannBCs both applied to the same sideset using
# two parsed functions.  The scale of the linear and constant functions
# are being parameterized.

[Optimization]
[]

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 10
  ny = 20
  xmax = 1
  ymax = 2
  bias_x = 1.1
  bias_y = 1.1
[]

[OptimizationReporter]
  type = GeneralOptimization
  objective_name = objective_value
  parameter_names = 'left right'
  num_values = '2 1'
[]
[Reporters]
  [main]
    type = OptimizationData
    file_xcoord = 'coordx'
    file_ycoord = 'y'
    file_zcoord = 'z'
    file_value = 'weightedMeasurement'
    file_variable_weights = 'weight'
    measurement_file = 'measurementData.csv'
  []
[]

[Executioner]
  type = Optimize
  tao_solver = taonls
  petsc_options_iname = '-tao_gttol -tao_nls_pc_type -tao_nls_ksp_type'
  petsc_options_value = '1e-3 none cg'
  verbose = true
[]

[MultiApps]
  [forward]
    type = FullSolveMultiApp
    input_files = forward.i
    execute_on = "FORWARD"
    clone_parent_mesh = true
  []
  [adjoint]
    type = FullSolveMultiApp
    input_files = adjoint.i
    execute_on = "ADJOINT"
    clone_parent_mesh = true
  []
  [homogeneousForward]
    type = FullSolveMultiApp
    input_files = homogeneous_forward.i
    execute_on = "HOMOGENEOUS_FORWARD"
    clone_parent_mesh = true
  []
[]

[Transfers]
  [toForward]
    type = MultiAppReporterTransfer
    to_multi_app = forward
    from_reporters = 'main/measurement_xcoord
                      main/measurement_ycoord
                      main/measurement_zcoord
                      main/measurement_time
                      main/measurement_values
                      main/weight
                      OptimizationReporter/left
                      OptimizationReporter/right'
    to_reporters = 'measure_data/measurement_xcoord
                    measure_data/measurement_ycoord
                    measure_data/measurement_zcoord
                    measure_data/measurement_time
                    measure_data/measurement_values
                    measure_data/weightForTemperature
                    params_left/vals
                    params_right/vals'
  []
  [fromForward]
    type = MultiAppReporterTransfer
    from_multi_app = forward
    from_reporters = 'measure_data/misfit_values measure_data/objective_value'
    to_reporters = 'main/misfit_values OptimizationReporter/objective_value'
  []
  [toAdjoint]
    type = MultiAppReporterTransfer
    to_multi_app = adjoint
    from_reporters = 'main/measurement_xcoord
                      main/measurement_ycoord
                      main/measurement_zcoord
                      main/measurement_time
                      main/misfit_values
                      main/weight
                      OptimizationReporter/left
                      OptimizationReporter/right'
    to_reporters = 'misfit/measurement_xcoord
                    misfit/measurement_ycoord
                    misfit/measurement_zcoord
                    misfit/measurement_time
                    misfit/misfit_values
                    misfit/weight
                    params_left/vals
                    params_right/vals'
  []
  [fromadjoint]
    type = MultiAppReporterTransfer
    from_multi_app = adjoint
    from_reporters = 'grad_bc_left/inner_product
                      grad_bc_right/inner_product'
    to_reporters = 'OptimizationReporter/grad_left
                    OptimizationReporter/grad_right'
  []

  # HESSIAN transfers.  Same as forward.
  [toHomogeneousForward]
    type = MultiAppReporterTransfer
    to_multi_app = homogeneousForward
    from_reporters = 'main/measurement_xcoord
                      main/measurement_ycoord
                      main/measurement_zcoord
                      main/measurement_time
                      main/measurement_values
                      main/weight
                      OptimizationReporter/left
                      OptimizationReporter/right'
    to_reporters = 'measure_data/measurement_xcoord
                    measure_data/measurement_ycoord
                    measure_data/measurement_zcoord
                    measure_data/measurement_time
                    measure_data/measurement_values
                    measure_data/weightForTemperature
                    params_left/vals
                    params_right/vals'
  []
  [fromHomogeneousForward]
    type = MultiAppReporterTransfer
    from_multi_app = homogeneousForward
    from_reporters = 'measure_data/simulation_values'
    to_reporters = 'main/misfit_values'
  []
[]

[Reporters]
  [optInfo]
    type = OptimizationInfo
    items = 'current_iterate function_value gnorm'
  []
[]

[Outputs]
  csv = true
  console = false
[]

(modules/combined/test/tests/optimization/invOpt_elasticity_modular/main.i)

[Optimization]
[]

[OptimizationReporter]
  type = GeneralOptimization
  objective_name = objective_value
  parameter_names = 'youngs_modulus'
  num_values = '3'
  initial_condition = '5.0 5.0 5.0'
  lower_bounds = '0.1'
  upper_bounds = '10.0'
[]

[Reporters]
  [main]
    type = OptimizationData
    measurement_points = '-1.0 -1.0 0.0
                          -1.0  0.0 0.0
                          -1.0  1.0 0.0
                           0.0 -1.0 0.0
                           0.0  0.0 0.0
                           0.0  1.0 0.0
                           1.0 -1.0 0.0
                           1.0  0.0 0.0
                           1.0  1.0 0.0'
    measurement_values = '3.276017e+00 4.763281e+00 6.380137e+00 3.171603e+00 4.660766e+00 6.289842e+00 3.127077e+00 4.608134e+00 6.228638e+00'
  []
[]

[Executioner]
  type = Optimize
  tao_solver = taobqnls #taobncg #taoblmvm
  petsc_options_iname = '-tao_gatol -tao_ls_type -tao_max_it'
  petsc_options_value = '1e-10 unit 1000'

  # THESE OPTIONS ARE FOR TESTING THE ADJOINT GRADIENT
  # petsc_options_iname = '-tao_max_it -tao_fd_test -tao_test_gradient -tao_fd_gradient -tao_fd_delta -tao_gatol'
  # petsc_options_value = '1 true true false 1e-8 0.1'
  # petsc_options = '-tao_test_gradient_view'
  # verbose = true
[]

[MultiApps]
  [forward]
    type = FullSolveMultiApp
    input_files = forward.i
    execute_on = FORWARD
  []
  [adjoint]
    type = FullSolveMultiApp
    input_files = grad.i
    execute_on = ADJOINT
  []
[]

[Transfers]
  [toForward]
    type = MultiAppReporterTransfer
    to_multi_app = forward
    from_reporters = 'main/measurement_xcoord
                      main/measurement_ycoord
                      main/measurement_zcoord
                      main/measurement_time
                      main/measurement_values
                      OptimizationReporter/youngs_modulus'
    to_reporters = 'measure_data/measurement_xcoord
                    measure_data/measurement_ycoord
                    measure_data/measurement_zcoord
                    measure_data/measurement_time
                    measure_data/measurement_values
                    parametrization/youngs_modulus'
  []
  [get_misfit]
    type = MultiAppReporterTransfer
    from_multi_app = forward
    from_reporters = 'measure_data/misfit_values measure_data/objective_value'
    to_reporters = 'main/misfit_values OptimizationReporter/objective_value'
  []
  [set_state_for_adjoint]
    type = MultiAppCopyTransfer
    from_multi_app = forward
    to_multi_app = adjoint
    source_variable = 'ux uy'
    variable = 'state_x state_y'
  []
  [setup_adjoint_run]
    type = MultiAppReporterTransfer
    to_multi_app = adjoint
    from_reporters = 'main/measurement_xcoord
                      main/measurement_ycoord
                      main/measurement_zcoord
                      main/measurement_time
                      main/misfit_values
                      OptimizationReporter/youngs_modulus'
    to_reporters = 'misfit/measurement_xcoord
                    misfit/measurement_ycoord
                    misfit/measurement_zcoord
                    misfit/measurement_time
                    misfit/misfit_values
                    parametrization/youngs_modulus'
  []
  [get_grad_youngs_modulus]
    type = MultiAppReporterTransfer
    from_multi_app = adjoint
    from_reporters = 'grad_youngs_modulus/inner_product'
    to_reporters = 'OptimizationReporter/grad_youngs_modulus'
  []
[]

[Reporters]
  [optInfo]
    type = OptimizationInfo
    items = 'current_iterate function_value gnorm'
  []
[]

[Outputs]
  console = false
  csv = true
[]

(modules/optimization/test/tests/outputs/exodus_optimization_steady/main_auto_adjoint.i)

[Optimization]
[]

[OptimizationReporter]
  type = GeneralOptimization
  objective_name = objective_value
  parameter_names = 'parameter_results'
  num_values = '3'
[]

[Reporters]
  [main]
    type = OptimizationData
    measurement_points = '0.5 0.28 0
0.5 0.6 0
0.5 0.8 0
0.5 1.1 0'
    measurement_values = '293 304 315 320'
  []
[]

[Executioner]
  type = Optimize
  tao_solver = taolmvm
  petsc_options_iname = '-tao_gttol -tao_ls_type'
  petsc_options_value = '1e-5 unit'
  verbose = true
[]

[MultiApps]
  [forward]
    type = FullSolveMultiApp
    input_files = forward_and_adjoint_iteration_output.i
    execute_on = "FORWARD"
  []
[]

[Transfers]
  # FORWARD transfers
  [toForward_measument]
    type = MultiAppReporterTransfer
    to_multi_app = forward
    from_reporters = 'main/measurement_xcoord
                      main/measurement_ycoord
                      main/measurement_zcoord
                      main/measurement_time
                      main/measurement_values
                      OptimizationReporter/parameter_results'
    to_reporters = 'measure_data/measurement_xcoord
                    measure_data/measurement_ycoord
                    measure_data/measurement_zcoord
                    measure_data/measurement_time
                    measure_data/measurement_values
                    point_source/value'
  []
  [fromForward]
    type = MultiAppReporterTransfer
    from_multi_app = forward
    from_reporters = 'measure_data/objective_value
                      gradient/temperature_adjoint'
    to_reporters = 'OptimizationReporter/objective_value
                    OptimizationReporter/grad_parameter_results'
  []
[]

[Outputs]
  csv = true
[]

(modules/optimization/test/tests/optimizationreporter/bc_load_linearFunction/main_auto_adjoint.i)

# This tests that a linear and constant function can be scaled in
# two separate functionNeumannBCs both applied to the same sideset using
# two parsed functions.  The scale of the linear and constant functions
# are being parameterized.

[Optimization]
[]

[OptimizationReporter]
  type = GeneralOptimization
  parameter_names = 'left right'
  num_values = '2 1'
  objective_name = obj_value
[]

[Executioner]
  type = Optimize
  tao_solver = taobqnls
  petsc_options_iname = '-tao_gatol -tao_ls_type'
  petsc_options_value = '1e-5 unit'
  verbose = true
[]

[MultiApps]
  [forward]
    type = FullSolveMultiApp
    input_files = forward_and_adjoint.i
    execute_on = "FORWARD"
  []
[]

[Transfers]
  [toForward]
    type = MultiAppReporterTransfer
    to_multi_app = forward
    from_reporters = 'OptimizationReporter/left
                      OptimizationReporter/right'
    to_reporters = 'params/left
                    params/right'
  []
  [fromForward]
    type = MultiAppReporterTransfer
    from_multi_app = forward
    from_reporters = 'obj_sum/value
                      grad_bc_left/inner_product
                      grad_bc_right/inner_product'
    to_reporters = 'OptimizationReporter/obj_value
                    OptimizationReporter/grad_left
                    OptimizationReporter/grad_right'
  []
[]

(modules/optimization/test/tests/reporters/multiExperiment/optimize.i)

[Optimization]
[]

[OptimizationReporter]
  type = GeneralOptimization
  parameter_names = 'vals'
  num_values = '2'
  objective_name = obj_value
[]

[Executioner]
  type = Optimize
  tao_solver = taobqnktr
  petsc_options_iname = '-tao_gatol'
  petsc_options_value = '1e-8 '
  verbose = true
[]

[MultiApps]
  [forward_sampler]
    type = FullSolveMultiApp
    input_files = sampler_subapp.i
    execute_on = FORWARD
  []
[]

[Transfers]
  [toForward]
    type = MultiAppReporterTransfer
    to_multi_app = forward_sampler
    from_reporters = 'OptimizationReporter/vals'
    to_reporters = 'parameters/vals'
  []

  [fromForward]
    type = MultiAppReporterTransfer
    from_multi_app = forward_sampler
    from_reporters = 'obj_sum/value
                      grad_sum/row_sum'
    to_reporters = 'OptimizationReporter/obj_value
                    OptimizationReporter/grad_vals'
  []
[]

[Outputs]
  csv = true
[]

(modules/optimization/examples/simpleTransient/main_gradient.i)

[Optimization]
[]

[OptimizationReporter]
  type = GeneralOptimization
  objective_name = objective_value
  parameter_names = 'source'
  num_values = '44'
[]

[Reporters]
  [main]
    type = OptimizationData
  []
[]

[MultiApps]
  [forward]
    type = FullSolveMultiApp
    input_files = forward.i
    execute_on = FORWARD
  []
  [adjoint]
    type = FullSolveMultiApp
    input_files = adjoint.i
    execute_on = ADJOINT
  []
[]

[Transfers]
  [to_forward]
    type = MultiAppReporterTransfer
    to_multi_app = forward
    from_reporters = 'OptimizationReporter/source'
    to_reporters = 'src_values/values'
  []
  [from_forward]
    type = MultiAppReporterTransfer
    from_multi_app = forward
    from_reporters = 'measured_data/misfit_values measured_data/objective_value'
    to_reporters = 'main/misfit_values OptimizationReporter/objective_value'
  []
  [to_adjoint]
    type = MultiAppReporterTransfer
    to_multi_app = adjoint
    from_reporters = 'OptimizationReporter/source main/misfit_values'
    to_reporters = 'src_values/values measured_data/misfit_values'
  []
  [from_adjoint]
    type = MultiAppReporterTransfer
    from_multi_app = adjoint
    from_reporters = 'adjoint/inner_product'
    to_reporters = 'OptimizationReporter/grad_source'
  []
[]

[Executioner]
  type = Optimize
  solve_on = none
  tao_solver = taolmvm
  petsc_options_iname = '-tao_gatol -tao_ls_type'
  petsc_options_value = '1e-2 unit'
  verbose = true
[]

[Postprocessors]
  [elapsed]
    type = PerfGraphData
    section_name = "Root"
    data_type = total
  []
[]

[Outputs]
  [pgraph]
    type = PerfGraphOutput
    level = 1
  []
[]

(modules/combined/test/tests/optimization/invOpt_mechanics/main.i)

[Optimization]
[]

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 10
  ny = 2
  xmin = 0.0
  xmax = 5.0
  ymin = 0.0
  ymax = 1.0
[]

[OptimizationReporter]
  type = GeneralOptimization
  objective_name = objective_value
  parameter_names = 'fy_right'
  num_values = '1'
  initial_condition = '100'
[]

[Reporters]
  [main]
    type = OptimizationData
    measurement_points = '5.0 1.0 0.0'
    measurement_values = '80.9'
  []
[]

[Executioner]
  type = Optimize
  tao_solver = taonls
  petsc_options_iname = '-tao_gttol -tao_max_it -tao_nls_pc_type -tao_nls_ksp_type'
  petsc_options_value = '1e-5 50 none cg'
  verbose = true
[]

[MultiApps]
  [forward]
    type = FullSolveMultiApp
    input_files = forward.i
    execute_on = "FORWARD"
    clone_parent_mesh = true
  []
  [adjoint]
    type = FullSolveMultiApp
    input_files = adjoint.i
    execute_on = "ADJOINT"
    clone_parent_mesh = true
  []
  # the forward problem has homogeneous boundary conditions so it can be reused here.
  [homogeneousForward]
    type = FullSolveMultiApp
    input_files = forward.i
    execute_on = "HOMOGENEOUS_FORWARD"
    clone_parent_mesh = true
  []
[]

[Transfers]
  [toForward_measument]
    type = MultiAppReporterTransfer
    to_multi_app = forward
    from_reporters = 'main/measurement_xcoord
                      main/measurement_ycoord
                      main/measurement_zcoord
                      main/measurement_time
                      main/measurement_values
                      OptimizationReporter/fy_right'
    to_reporters = 'measure_data/measurement_xcoord
                    measure_data/measurement_ycoord
                    measure_data/measurement_zcoord
                    measure_data/measurement_time
                    measure_data/measurement_values
                    params/right_fy_value'
  []
  [fromForward]
    type = MultiAppReporterTransfer
    from_multi_app = forward
    from_reporters = 'measure_data/misfit_values measure_data/objective_value'
    to_reporters = 'main/misfit_values OptimizationReporter/objective_value'
  []
  [toAdjoint]
    type = MultiAppReporterTransfer
    to_multi_app = adjoint
    from_reporters = 'main/measurement_xcoord
                      main/measurement_ycoord
                      main/measurement_zcoord
                      main/measurement_time
                      main/misfit_values
                      OptimizationReporter/fy_right'
    to_reporters = 'misfit/measurement_xcoord
                    misfit/measurement_ycoord
                    misfit/measurement_zcoord
                    misfit/measurement_time
                    misfit/misfit_values
                    params/right_fy_value'
  []
  [fromAdjoint]
    type = MultiAppReporterTransfer
    from_multi_app = adjoint
    from_reporters = 'adjoint_pt/inner_product'
    to_reporters = 'OptimizationReporter/grad_fy_right'
  []

  [toHomogeneousForward_measument]
    type = MultiAppReporterTransfer
    to_multi_app = homogeneousForward
    from_reporters = 'main/measurement_xcoord
                      main/measurement_ycoord
                      main/measurement_zcoord
                      main/measurement_time
                      main/measurement_values
                      OptimizationReporter/fy_right'
    to_reporters = 'measure_data/measurement_xcoord
                    measure_data/measurement_ycoord
                    measure_data/measurement_zcoord
                    measure_data/measurement_time
                    measure_data/measurement_values
                    params/right_fy_value'
  []
  [fromHomogeneousForward]
    type = MultiAppReporterTransfer
    from_multi_app = homogeneousForward
    from_reporters = 'measure_data/simulation_values'
    to_reporters = 'main/misfit_values'
  []
[]

[Reporters]
  [optInfo]
    type = OptimizationInfo
  []
[]

[Outputs]
  csv = true
[]

(modules/optimization/test/tests/optimizationreporter/point_loads/main_auto_adjoint.i)

measurement_points = '0.5 0.28 0
   0.5 0.6 0
   0.5 0.8 0
   0.5 1.1 0'
measurement_values = '293 304 315 320'

[Optimization]
[]

[OptimizationReporter]
  type = GeneralOptimization
  objective_name = objective_value
  parameter_names = 'parameter_results'
  num_values = '3'
[]

[Reporters]
  [main]
    type = OptimizationData
    measurement_points = ${measurement_points}
    measurement_values = ${measurement_values}
  []
[]

[Executioner]
  type = Optimize
  tao_solver = taolmvm
  petsc_options_iname = '-tao_gttol -tao_ls_type'
  petsc_options_value = '1e-5 unit'
  verbose = true
[]

[MultiApps]
  [forward]
    type = FullSolveMultiApp
    input_files = forward_and_adjoint.i
    execute_on = "FORWARD"
  []
[]

[Transfers]
  # FORWARD transfers
  [toForward_measument]
    type = MultiAppReporterTransfer
    to_multi_app = forward
    from_reporters = 'main/measurement_xcoord
                      main/measurement_ycoord
                      main/measurement_zcoord
                      main/measurement_time
                      main/measurement_values
                      OptimizationReporter/parameter_results'
    to_reporters = 'measure_data/measurement_xcoord
                    measure_data/measurement_ycoord
                    measure_data/measurement_zcoord
                    measure_data/measurement_time
                    measure_data/measurement_values
                    point_source/value'
  []
  [fromForward]
    type = MultiAppReporterTransfer
    from_multi_app = forward
    from_reporters = 'measure_data/objective_value
                      gradient/temperature_adjoint'
    to_reporters = 'OptimizationReporter/objective_value
                    OptimizationReporter/grad_parameter_results'
  []
[]

[Outputs]
  csv = true
[]

(modules/combined/test/tests/optimization/invOpt_nonlinear/main.i)

[Optimization]
[]

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 10
  ny = 10
  xmax = 2
  ymax = 2
[]

[OptimizationReporter]
  type = GeneralOptimization
  objective_name = objective_value
  parameter_names = 'heat_source'
  num_values = '1'
  initial_condition = '0'
  lower_bounds = '0.1'
  upper_bounds = '10000'
[]

[Reporters]
  [main]
    type = OptimizationData
    measurement_points = '0.2 0.2 0
                          0.8 0.6 0
                          0.2 1.4 0
                          0.8 1.8 0'
    measurement_values = '1.98404 1.91076 1.56488 1.23863'
  []
[]

[Executioner]
  type = Optimize
  tao_solver = taonls
  petsc_options_iname = '-tao_gttol -tao_max_it -tao_nls_pc_type -tao_nls_ksp_type'
  petsc_options_value = ' 1e-5       5           none             cg'
  verbose = true
[]

[MultiApps]
  [forward]
    type = FullSolveMultiApp
    input_files = forward.i
    execute_on = FORWARD
    clone_parent_mesh = true
  []
  [homogeneous_forward]
    type = FullSolveMultiApp
    input_files = homogeneous_forward.i
    execute_on = HOMOGENEOUS_FORWARD
    clone_parent_mesh = true
  []
  [adjoint]
    type = FullSolveMultiApp
    input_files = adjoint.i
    execute_on = ADJOINT
    clone_parent_mesh = true
  []
[]

[Transfers]
  ## RUN FORWARD SIMULATION WITH CURRENT PARAMETERS AS FORCE,
  ## AND EXTRACT SIMULATED VALUES AT MEASUREMENT POINTS
  ## AS WELL AS TOTAL FIELD VARIABLE FOR NONLINEAR PURPOSES
  [MeasurementLocationsToForward]
    type = MultiAppReporterTransfer
    to_multi_app = forward
    from_reporters = 'main/measurement_xcoord
                      main/measurement_ycoord
                      main/measurement_zcoord
                      main/measurement_time
                      main/measurement_values
                      OptimizationReporter/heat_source'
    to_reporters = 'measurement_locations/measurement_xcoord
                    measurement_locations/measurement_ycoord
                    measurement_locations/measurement_zcoord
                    measurement_locations/measurement_time
                    measurement_locations/measurement_values
                    params/heat_source'
  []
  [SimulatedDataFromForward]
    type = MultiAppReporterTransfer
    from_multi_app = forward
    from_reporters = 'measurement_locations/misfit_values measurement_locations/objective_value'
    to_reporters = 'main/misfit_values OptimizationReporter/objective_value'
  []
  ### RUN THE HOMOGENEOUS_FORWARD WITH CURRENT NONLINEAR STATE, PARAMETER_STEP,
  ### AND EXTRACT SIMULATED DATA AT MEASURMENT POINTS
  [CurrentStateFromForwardNonlinearToHomogeneousForwardNonlinear]
    type = MultiAppCopyTransfer
    from_multi_app = forward
    to_multi_app = homogeneous_forward
    source_variable = 'forwardT'
    variable = 'forwardT'
  []
  [MeasurementLocationsToHomogeneousForward]
    type = MultiAppReporterTransfer
    to_multi_app = homogeneous_forward
    from_reporters = 'main/measurement_xcoord
                      main/measurement_ycoord
                      main/measurement_zcoord
                      main/measurement_time
                      main/measurement_values
                      OptimizationReporter/heat_source'
    to_reporters = 'measurement_locations/measurement_xcoord
                    measurement_locations/measurement_ycoord
                    measurement_locations/measurement_zcoord
                    measurement_locations/measurement_time
                    measurement_locations/measurement_values
                    params/heat_source'
  []
  [SimulatedDataFromHomogeneousForward]
    type = MultiAppReporterTransfer
    from_multi_app = homogeneous_forward
    from_reporters = 'measurement_locations/simulation_values'
    to_reporters = 'main/misfit_values'
  []
  ### RUN THE ADJOINT WITH CURRENT NONLINEAR STATE, WITH MISFIT AS EXCITATION,
  ### AND EXTRACT GRADIENT
  [CurrentStateToAdjointNonlinear]
    type = MultiAppCopyTransfer
    from_multi_app = forward
    to_multi_app = adjoint
    source_variable = 'forwardT'
    variable = 'forwardT'
  []
  [MisfitToAdjoint]
    type = MultiAppReporterTransfer
    to_multi_app = adjoint
    from_reporters = 'main/measurement_xcoord
                      main/measurement_ycoord
                      main/measurement_zcoord
                      main/measurement_time
                      main/misfit_values
                      OptimizationReporter/heat_source'
    to_reporters = 'misfit/measurement_xcoord
                    misfit/measurement_ycoord
                    misfit/measurement_zcoord
                    misfit/measurement_time
                    misfit/misfit_values
                    params/heat_source'
  []
  [GradientFromAdjoint]
    type = MultiAppReporterTransfer
    from_multi_app = adjoint
    from_reporters = 'gradient_vpp/inner_product'
    to_reporters = 'OptimizationReporter/grad_heat_source'
  []
[]

[Reporters]
  [optInfo]
    type = OptimizationInfo
  []
[]

[Outputs]
  csv = true
[]

Overview
Example Input Syntax
Input Parameters
Input Files