OptimizeSolve.C

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//* This file is part of the MOOSE framework
//* https://mooseframework.inl.gov
//*
//* 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
 
#include "Moose.h"
#include "MooseError.h"
#include "OptimizeSolve.h"
#include "OptimizationAppTypes.h"
#include "OptimizationReporterBase.h"
#include "Steady.h"
 
InputParameters
OptimizeSolve::validParams()
{
  InputParameters params = emptyInputParameters();
  MooseEnum tao_solver_enum("taontr taobntr taobncg taonls taobnls taobqnktr taontl taobntl "
                            "taonm taobqnls taoowlqn taogpcg taobmrm taoalmm");
  params.addRequiredParam<MooseEnum>(
      "tao_solver", tao_solver_enum, "Tao solver to use for optimization.");
  ExecFlagEnum exec_enum = ExecFlagEnum();
  exec_enum.addAvailableFlags(EXEC_NONE,
                              OptimizationAppTypes::EXEC_FORWARD,
                              OptimizationAppTypes::EXEC_ADJOINT,
                              OptimizationAppTypes::EXEC_HOMOGENEOUS_FORWARD);
  exec_enum = {OptimizationAppTypes::EXEC_FORWARD,
               OptimizationAppTypes::EXEC_ADJOINT,
               OptimizationAppTypes::EXEC_HOMOGENEOUS_FORWARD};
  params.addParam<ExecFlagEnum>(
      "solve_on", exec_enum, "List of flags indicating when inner system solve should occur.");
  params.addParam<bool>(
      "output_optimization_iterations",
      false,
      "Use the time step as the current iteration for outputting optimization history.");
  return params;
}
 
OptimizeSolve::OptimizeSolve(Executioner & ex)
  : SolveObject(ex),
    _my_comm(MPI_COMM_SELF),
    _solve_on(getParam<ExecFlagEnum>("solve_on")),
    _verbose(getParam<bool>("verbose")),
    _output_opt_iters(getParam<bool>("output_optimization_iterations")),
    _tao_solver_enum(getParam<MooseEnum>("tao_solver").getEnum<TaoSolverEnum>()),
    _parameters(std::make_unique<libMesh::PetscVector<Number>>(_my_comm))
{
  if (_problem.numThreads() > 1)
    mooseError("OptimizeSolve does not currently support threaded execution");
 
  if (_output_opt_iters && _problem.isTransient())
    mooseDocumentedError(
        "moose", 27225, "Outputting for transient executioners has not been implemented.");
}
 
bool
OptimizeSolve::solve()
{
  TIME_SECTION("optimizeSolve", 1, "Optimization Solve");
  // Initial solve
  _inner_solve->solve();
 
  // Grab objective function
  if (!_problem.hasUserObject("OptimizationReporter"))
    mooseError("No OptimizationReporter object found.");
  _obj_function = &_problem.getUserObject<OptimizationReporterBase>("OptimizationReporter");
 
  // Initialize solution and matrix
  _obj_function->setInitialCondition(*_parameters);
  _ndof = _parameters->size();
 
  // time step defaults 1, we want to start at 0 for first iteration to be
  // consistent with TAO iterations.
  if (_output_opt_iters)
    _problem.timeStep() = 0;
  bool solveInfo = (taoSolve() == 0);
  return solveInfo;
}
 
PetscErrorCode
OptimizeSolve::taoSolve()
{
  PetscFunctionBegin;
  // Initialize tao object
  LibmeshPetscCallQ(TaoCreate(_my_comm.get(), &_tao));
 
#if PETSC_RELEASE_LESS_THAN(3, 21, 0)
  LibmeshPetscCallQ(TaoSetMonitor(_tao, monitor, this, nullptr));
#else
  LibmeshPetscCallQ(TaoMonitorSet(_tao, monitor, this, nullptr));
#endif
 
  switch (_tao_solver_enum)
  {
    case TaoSolverEnum::NEWTON_TRUST_REGION:
      LibmeshPetscCallQ(TaoSetType(_tao, TAONTR));
      break;
    case TaoSolverEnum::BOUNDED_NEWTON_TRUST_REGION:
      LibmeshPetscCallQ(TaoSetType(_tao, TAOBNTR));
      break;
    case TaoSolverEnum::BOUNDED_CONJUGATE_GRADIENT:
      LibmeshPetscCallQ(TaoSetType(_tao, TAOBNCG));
      break;
    case TaoSolverEnum::NEWTON_LINE_SEARCH:
      LibmeshPetscCallQ(TaoSetType(_tao, TAONLS));
      break;
    case TaoSolverEnum::BOUNDED_NEWTON_LINE_SEARCH:
      LibmeshPetscCallQ(TaoSetType(_tao, TAOBNLS));
      break;
    case TaoSolverEnum::BOUNDED_QUASI_NEWTON_TRUST_REGION:
      LibmeshPetscCallQ(TaoSetType(_tao, TAOBQNKTR));
      break;
    case TaoSolverEnum::NEWTON_TRUST_LINE:
      LibmeshPetscCallQ(TaoSetType(_tao, TAONTL));
      break;
    case TaoSolverEnum::BOUNDED_NEWTON_TRUST_LINE:
      LibmeshPetscCallQ(TaoSetType(_tao, TAOBNTL));
      break;
    case TaoSolverEnum::NELDER_MEAD:
      LibmeshPetscCallQ(TaoSetType(_tao, TAONM));
      break;
 
    case TaoSolverEnum::BOUNDED_QUASI_NEWTON_LINE_SEARCH:
      LibmeshPetscCallQ(TaoSetType(_tao, TAOBQNLS));
      break;
    case TaoSolverEnum::ORTHANT_QUASI_NEWTON:
      LibmeshPetscCallQ(TaoSetType(_tao, TAOOWLQN));
      break;
    case TaoSolverEnum::GRADIENT_PROJECTION_CONJUGATE_GRADIENT:
      LibmeshPetscCallQ(TaoSetType(_tao, TAOGPCG));
      break;
    case TaoSolverEnum::BUNDLE_RISK_MIN:
      LibmeshPetscCallQ(TaoSetType(_tao, TAOBMRM));
      break;
    case TaoSolverEnum::AUGMENTED_LAGRANGIAN_MULTIPLIER_METHOD:
#if !PETSC_VERSION_LESS_THAN(3, 15, 0)
      LibmeshPetscCallQ(TaoSetType(_tao, TAOALMM));
      // Need to cancel monitors for ALMM, if not there is a segfault at MOOSE destruction. Setup
      // default constraint monitor.
#if PETSC_RELEASE_GREATER_EQUALS(3, 21, 0)
      LibmeshPetscCallQ(TaoMonitorCancel(_tao));
#else
      LibmeshPetscCallQ(TaoCancelMonitors(_tao));
#endif
      LibmeshPetscCallQ(PetscOptionsSetValue(NULL, "-tao_cmonitor", NULL));
      break;
#else
      mooseError("ALMM is only compatible with PETSc versions above 3.14. ");
#endif
 
    default:
      mooseError("Invalid Tao solve type");
  }
 
    // Set objective and gradient functions
#if !PETSC_VERSION_LESS_THAN(3, 17, 0)
  LibmeshPetscCallQ(TaoSetObjective(_tao, objectiveFunctionWrapper, this));
#else
  LibmeshPetscCallQ(TaoSetObjectiveRoutine(_tao, objectiveFunctionWrapper, this));
#endif
#if !PETSC_VERSION_LESS_THAN(3, 17, 0)
  LibmeshPetscCallQ(
      TaoSetObjectiveAndGradient(_tao, NULL, objectiveAndGradientFunctionWrapper, this));
#else
  LibmeshPetscCallQ(
      TaoSetObjectiveAndGradientRoutine(_tao, objectiveAndGradientFunctionWrapper, this));
#endif
 
  // Set matrix-free version of the Hessian function
  LibmeshPetscCallQ(MatCreateShell(_my_comm.get(), _ndof, _ndof, _ndof, _ndof, this, &_hessian));
  // Link matrix-free Hessian to Tao
#if !PETSC_VERSION_LESS_THAN(3, 17, 0)
  LibmeshPetscCallQ(TaoSetHessian(_tao, _hessian, _hessian, hessianFunctionWrapper, this));
#else
  LibmeshPetscCallQ(TaoSetHessianRoutine(_tao, _hessian, _hessian, hessianFunctionWrapper, this));
#endif
 
  // Set initial guess
#if !PETSC_VERSION_LESS_THAN(3, 17, 0)
  LibmeshPetscCallQ(TaoSetSolution(_tao, _parameters->vec()));
#else
  LibmeshPetscCallQ(TaoSetInitialVector(_tao, _parameters->vec()));
#endif
 
  // Set TAO petsc options
  LibmeshPetscCallQ(TaoSetFromOptions(_tao));
 
  // save nonTAO PETSC options to reset before every call to execute()
  _petsc_options = _problem.getPetscOptions();
  // We only use a single system solve at this point
  _solver_params = _problem.solverParams(0);
 
  // Set bounds for bounded optimization
  LibmeshPetscCallQ(TaoSetVariableBoundsRoutine(_tao, variableBoundsWrapper, this));
 
  if (_tao_solver_enum == TaoSolverEnum::AUGMENTED_LAGRANGIAN_MULTIPLIER_METHOD)
    LibmeshPetscCallQ(taoALCreate());
 
  // Backup multiapps so transient problems start with the same initial condition
  _problem.backupMultiApps(OptimizationAppTypes::EXEC_FORWARD);
  _problem.backupMultiApps(OptimizationAppTypes::EXEC_ADJOINT);
  _problem.backupMultiApps(OptimizationAppTypes::EXEC_HOMOGENEOUS_FORWARD);
 
  // Solve optimization
  LibmeshPetscCallQ(TaoSolve(_tao));
 
  // Print solve statistics
  if (getParam<bool>("verbose"))
    LibmeshPetscCallQ(TaoView(_tao, PETSC_VIEWER_STDOUT_WORLD));
 
  LibmeshPetscCallQ(TaoDestroy(&_tao));
 
  LibmeshPetscCallQ(MatDestroy(&_hessian));
 
  if (_tao_solver_enum == TaoSolverEnum::AUGMENTED_LAGRANGIAN_MULTIPLIER_METHOD)
    LibmeshPetscCallQ(taoALDestroy());
 
  PetscFunctionReturn(PETSC_SUCCESS);
}
 
void
OptimizeSolve::getTaoSolutionStatus(std::vector<int> & tot_iters,
                                    std::vector<double> & gnorm,
                                    std::vector<int> & obj_iters,
                                    std::vector<double> & cnorm,
                                    std::vector<int> & grad_iters,
                                    std::vector<double> & xdiff,
                                    std::vector<int> & hess_iters,
                                    std::vector<double> & f,
                                    std::vector<int> & tot_solves) const
{
  const auto num = _total_iterate_vec.size();
  tot_iters.resize(num);
  obj_iters.resize(num);
  grad_iters.resize(num);
  hess_iters.resize(num);
  tot_solves.resize(num);
  f.resize(num);
  gnorm.resize(num);
  cnorm.resize(num);
  xdiff.resize(num);
 
  for (const auto i : make_range(num))
  {
    tot_iters[i] = _total_iterate_vec[i];
    obj_iters[i] = _obj_iterate_vec[i];
    grad_iters[i] = _grad_iterate_vec[i];
    hess_iters[i] = _hess_iterate_vec[i];
    tot_solves[i] = _function_solve_vec[i];
    f[i] = _f_vec[i];
    gnorm[i] = _gnorm_vec[i];
    cnorm[i] = _cnorm_vec[i];
    xdiff[i] = _xdiff_vec[i];
  }
}
 
void
OptimizeSolve::setTaoSolutionStatus(double f, int its, double gnorm, double cnorm, double xdiff)
{
  // set data from TAO
  _total_iterate_vec.push_back(its);
  _f_vec.push_back(f);
  _gnorm_vec.push_back(gnorm);
  _cnorm_vec.push_back(cnorm);
  _xdiff_vec.push_back(xdiff);
  // set data we collect on this optimization iteration and then reset for next iteration
  _obj_iterate_vec.push_back(_obj_iterate);
  _grad_iterate_vec.push_back(_grad_iterate);
  _hess_iterate_vec.push_back(_hess_iterate);
  // count total number of FE solves
  int solves = _obj_iterate + _grad_iterate + 2 * _hess_iterate;
  _function_solve_vec.push_back(solves);
  _obj_iterate = 0;
  _grad_iterate = 0;
  _hess_iterate = 0;
 
  // Pass down the iteration number if the subapp is of the Steady/SteadyAndAdjoint type.
  // This enables exodus per-iteration output.
  for (auto & sub_app : _app.getExecutioner()->feProblem().getMultiAppWarehouse().getObjects())
  {
    if (auto steady = dynamic_cast<Steady *>(sub_app->getExecutioner(0)))
      steady->setIterationNumberOutput((unsigned int)its);
  }
 
  // Output the converged iteration outputs
  _problem.outputStep(OptimizationAppTypes::EXEC_FORWARD);
 
  // Increment timestep. In steady problems timestep = time for outputting.
  // See Output.C
  if (_output_opt_iters)
    _problem.timeStep() += 1;
 
  // print verbose per iteration output
  if (_verbose)
    _console << "TAO SOLVER: iteration=" << its << "\tf=" << f << "\tgnorm=" << gnorm
             << "\tcnorm=" << cnorm << "\txdiff=" << xdiff << std::endl;
}
 
PetscErrorCode
OptimizeSolve::monitor(Tao tao, void * ctx)
{
  TaoConvergedReason reason;
  PetscInt its;
  PetscReal f, gnorm, cnorm, xdiff;
 
  PetscFunctionBegin;
  LibmeshPetscCallQ(TaoGetSolutionStatus(tao, &its, &f, &gnorm, &cnorm, &xdiff, &reason));
 
  auto * solver = static_cast<OptimizeSolve *>(ctx);
  solver->setTaoSolutionStatus((double)f, (int)its, (double)gnorm, (double)cnorm, (double)xdiff);
 
  PetscFunctionReturn(PETSC_SUCCESS);
}
 
PetscErrorCode
OptimizeSolve::objectiveFunctionWrapper(Tao /*tao*/, Vec x, Real * objective, void * ctx)
{
  PetscFunctionBegin;
  auto * solver = static_cast<OptimizeSolve *>(ctx);
 
  libMesh::PetscVector<Number> param(x, solver->_my_comm);
  solver->_parameters->swap(param);
 
  (*objective) = solver->objectiveFunction();
  solver->_parameters->swap(param);
  PetscFunctionReturn(PETSC_SUCCESS);
}
 
PetscErrorCode
OptimizeSolve::objectiveAndGradientFunctionWrapper(
    Tao /*tao*/, Vec x, Real * objective, Vec gradient, void * ctx)
{
  PetscFunctionBegin;
  auto * solver = static_cast<OptimizeSolve *>(ctx);
 
  libMesh::PetscVector<Number> param(x, solver->_my_comm);
  solver->_parameters->swap(param);
 
  (*objective) = solver->objectiveFunction();
  libMesh::PetscVector<Number> grad(gradient, solver->_my_comm);
  solver->gradientFunction(grad);
  solver->_parameters->swap(param);
  PetscFunctionReturn(PETSC_SUCCESS);
}
 
PetscErrorCode
OptimizeSolve::hessianFunctionWrapper(
    Tao /*tao*/, Vec /*x*/, Mat /*hessian*/, Mat /*pc*/, void * ctx)
{
  PetscFunctionBegin;
  // Define Hessian-vector multiplication routine
  auto * solver = static_cast<OptimizeSolve *>(ctx);
  LibmeshPetscCallQ(MatShellSetOperation(
      solver->_hessian, MATOP_MULT, (void (*)(void))OptimizeSolve::applyHessianWrapper));
  PetscFunctionReturn(PETSC_SUCCESS);
}
 
PetscErrorCode
OptimizeSolve::applyHessianWrapper(Mat H, Vec s, Vec Hs)
{
  void * ctx;
 
  PetscFunctionBegin;
  LibmeshPetscCallQ(MatShellGetContext(H, &ctx));
 
  auto * solver = static_cast<OptimizeSolve *>(ctx);
  libMesh::PetscVector<Number> sbar(s, solver->_my_comm);
  libMesh::PetscVector<Number> Hsbar(Hs, solver->_my_comm);
  return solver->applyHessian(sbar, Hsbar);
}
 
PetscErrorCode
OptimizeSolve::variableBoundsWrapper(Tao tao, Vec /*xl*/, Vec /*xu*/, void * ctx)
{
  PetscFunctionBegin;
  auto * solver = static_cast<OptimizeSolve *>(ctx);
 
  LibmeshPetscCallQ(solver->variableBounds(tao));
  PetscFunctionReturn(PETSC_SUCCESS);
}
 
Real
OptimizeSolve::objectiveFunction()
{
  TIME_SECTION("objectiveFunction", 2, "Objective forward solve");
  _obj_function->updateParameters(*_parameters);
 
  Moose::PetscSupport::petscSetOptions(_petsc_options, _solver_params);
  _problem.execute(OptimizationAppTypes::EXEC_FORWARD);
 
  _problem.restoreMultiApps(OptimizationAppTypes::EXEC_FORWARD);
  if (!_problem.execMultiApps(OptimizationAppTypes::EXEC_FORWARD))
  {
    // We do this so we can output for failed solves.
    _problem.outputStep(OptimizationAppTypes::EXEC_FORWARD);
    mooseError("Forward solve multiapp failed!");
  }
  if (_solve_on.isValueSet(OptimizationAppTypes::EXEC_FORWARD))
    _inner_solve->solve();
 
  _obj_iterate++;
  return _obj_function->computeObjective();
}
 
void
OptimizeSolve::gradientFunction(libMesh::PetscVector<Number> & gradient)
{
  TIME_SECTION("gradientFunction", 2, "Gradient adjoint solve");
  _obj_function->updateParameters(*_parameters);
 
  Moose::PetscSupport::petscSetOptions(_petsc_options, _solver_params);
  _problem.execute(OptimizationAppTypes::EXEC_ADJOINT);
  _problem.restoreMultiApps(OptimizationAppTypes::EXEC_ADJOINT);
  if (!_problem.execMultiApps(OptimizationAppTypes::EXEC_ADJOINT))
    mooseError("Adjoint solve multiapp failed!");
  if (_solve_on.isValueSet(OptimizationAppTypes::EXEC_ADJOINT))
    _inner_solve->solve();
 
  _grad_iterate++;
  _obj_function->computeGradient(gradient);
}
 
PetscErrorCode
OptimizeSolve::applyHessian(libMesh::PetscVector<Number> & s, libMesh::PetscVector<Number> & Hs)
{
  PetscFunctionBegin;
  TIME_SECTION("applyHessian", 2, "Hessian forward/adjoint solve");
  // What happens for material inversion when the Hessian
  // is dependent on the parameters? Deal with it later???
  // see notes on how this needs to change for Material inversion
  if (_problem.hasMultiApps() &&
      !_problem.hasMultiApps(OptimizationAppTypes::EXEC_HOMOGENEOUS_FORWARD))
    mooseError("Hessian based optimization algorithms require a sub-app with:\n"
               "   execute_on = HOMOGENEOUS_FORWARD");
  _obj_function->updateParameters(s);
 
  Moose::PetscSupport::petscSetOptions(_petsc_options, _solver_params);
  _problem.execute(OptimizationAppTypes::EXEC_HOMOGENEOUS_FORWARD);
  _problem.restoreMultiApps(OptimizationAppTypes::EXEC_HOMOGENEOUS_FORWARD);
  if (!_problem.execMultiApps(OptimizationAppTypes::EXEC_HOMOGENEOUS_FORWARD))
    mooseError("Homogeneous forward solve multiapp failed!");
  if (_solve_on.isValueSet(OptimizationAppTypes::EXEC_HOMOGENEOUS_FORWARD))
    _inner_solve->solve();
 
  // The adjoint solve below applies the misfit as its source. For the Hessian action, that source
  // is the simulated values from the homogeneous forward solve, so the input must transfer
  // 'simulation_values' from the homogeneous forward sub-app into 'misfit_values'.
  Moose::PetscSupport::petscSetOptions(_petsc_options, _solver_params);
  _problem.execute(OptimizationAppTypes::EXEC_ADJOINT);
  _problem.restoreMultiApps(OptimizationAppTypes::EXEC_ADJOINT);
  if (!_problem.execMultiApps(OptimizationAppTypes::EXEC_ADJOINT))
    mooseError("Adjoint solve multiapp failed!");
  if (_solve_on.isValueSet(OptimizationAppTypes::EXEC_ADJOINT))
    _inner_solve->solve();
 
  _obj_function->computeGradient(Hs);
  _hess_iterate++;
  PetscFunctionReturn(PETSC_SUCCESS);
}
 
PetscErrorCode
OptimizeSolve::variableBounds(Tao tao)
{
  PetscFunctionBegin;
  unsigned int sz = _obj_function->getNumParams();
 
  libMesh::PetscVector<Number> xl(_my_comm, sz);
  libMesh::PetscVector<Number> xu(_my_comm, sz);
 
  // copy values from upper and lower bounds to xl and xu
  for (const auto i : make_range(sz))
  {
    xl.set(i, _obj_function->getLowerBound(i));
    xu.set(i, _obj_function->getUpperBound(i));
  }
  // set upper and lower bounds in tao solver
  LibmeshPetscCallQ(TaoSetVariableBounds(tao, xl.vec(), xu.vec()));
  PetscFunctionReturn(PETSC_SUCCESS);
}
 
PetscErrorCode
OptimizeSolve::equalityFunctionWrapper(Tao /*tao*/, Vec /*x*/, Vec ce, void * ctx)
{
  PetscFunctionBegin;
  // grab the solver
  auto * solver = static_cast<OptimizeSolve *>(ctx);
  libMesh::PetscVector<Number> eq_con(ce, solver->_my_comm);
  // use the OptimizationReporterBase class to actually compute equality constraints
  OptimizationReporterBase * obj_func = solver->getObjFunction();
  obj_func->computeEqualityConstraints(eq_con);
  PetscFunctionReturn(PETSC_SUCCESS);
}
 
PetscErrorCode
OptimizeSolve::equalityGradientFunctionWrapper(
    Tao /*tao*/, Vec /*x*/, Mat gradient_e, Mat /*gradient_epre*/, void * ctx)
{
  PetscFunctionBegin;
  // grab the solver
  auto * solver = static_cast<OptimizeSolve *>(ctx);
  libMesh::PetscMatrix<Number> grad_eq(gradient_e, solver->_my_comm);
  // use the OptimizationReporterBase class to actually compute equality
  // constraints gradient
  OptimizationReporterBase * obj_func = solver->getObjFunction();
  obj_func->computeEqualityGradient(grad_eq);
  PetscFunctionReturn(PETSC_SUCCESS);
}
 
PetscErrorCode
OptimizeSolve::inequalityFunctionWrapper(Tao /*tao*/, Vec /*x*/, Vec ci, void * ctx)
{
  PetscFunctionBegin;
  // grab the solver
  auto * solver = static_cast<OptimizeSolve *>(ctx);
  libMesh::PetscVector<Number> ineq_con(ci, solver->_my_comm);
  // use the OptimizationReporterBase class to actually compute equality constraints
  OptimizationReporterBase * obj_func = solver->getObjFunction();
  obj_func->computeInequalityConstraints(ineq_con);
  PetscFunctionReturn(PETSC_SUCCESS);
}
 
PetscErrorCode
OptimizeSolve::inequalityGradientFunctionWrapper(
    Tao /*tao*/, Vec /*x*/, Mat gradient_i, Mat /*gradient_ipre*/, void * ctx)
{
  PetscFunctionBegin;
  // grab the solver
  auto * solver = static_cast<OptimizeSolve *>(ctx);
  libMesh::PetscMatrix<Number> grad_ineq(gradient_i, solver->_my_comm);
  // use the OptimizationReporterBase class to actually compute equality
  // constraints gradient
  OptimizationReporterBase * obj_func = solver->getObjFunction();
  obj_func->computeInequalityGradient(grad_ineq);
  PetscFunctionReturn(PETSC_SUCCESS);
}
 
PetscErrorCode
OptimizeSolve::taoALCreate()
{
  PetscFunctionBegin;
  if (_obj_function->getNumEqCons())
  {
    // Create equality vector
    LibmeshPetscCallQ(VecCreate(_my_comm.get(), &_ce));
    LibmeshPetscCallQ(
        VecSetSizes(_ce, _obj_function->getNumEqCons(), _obj_function->getNumEqCons()));
    LibmeshPetscCallQ(VecSetFromOptions(_ce));
    LibmeshPetscCallQ(VecSetUp(_ce));
 
    // Set equality jacobian matrix
    LibmeshPetscCallQ(MatCreate(_my_comm.get(), &_gradient_e));
    LibmeshPetscCallQ(MatSetSizes(
        _gradient_e, _obj_function->getNumEqCons(), _ndof, _obj_function->getNumEqCons(), _ndof));
    LibmeshPetscCallQ(MatSetFromOptions(_gradient_e));
    LibmeshPetscCallQ(MatSetUp(_gradient_e));
 
    // Set the Equality Constraints
    LibmeshPetscCallQ(TaoSetEqualityConstraintsRoutine(_tao, _ce, equalityFunctionWrapper, this));
 
    // Set the Equality Constraints Jacobian
    LibmeshPetscCallQ(TaoSetJacobianEqualityRoutine(
        _tao, _gradient_e, _gradient_e, equalityGradientFunctionWrapper, this));
  }
 
  if (_obj_function->getNumInEqCons())
  {
    // Create inequality vector
    LibmeshPetscCallQ(VecCreate(_my_comm.get(), &_ci));
    LibmeshPetscCallQ(
        VecSetSizes(_ci, _obj_function->getNumInEqCons(), _obj_function->getNumInEqCons()));
    LibmeshPetscCallQ(VecSetFromOptions(_ci));
    LibmeshPetscCallQ(VecSetUp(_ci));
 
    // Set inequality jacobian matrix
    LibmeshPetscCallQ(MatCreate(_my_comm.get(), &_gradient_i));
    LibmeshPetscCallQ(MatSetSizes(_gradient_i,
                                  _obj_function->getNumInEqCons(),
                                  _ndof,
                                  _obj_function->getNumInEqCons(),
                                  _ndof));
    LibmeshPetscCallQ(MatSetFromOptions(_gradient_i));
    LibmeshPetscCallQ(MatSetUp(_gradient_i));
 
    // Set the Inequality constraints
    LibmeshPetscCallQ(
        TaoSetInequalityConstraintsRoutine(_tao, _ci, inequalityFunctionWrapper, this));
 
    // Set the Inequality constraints Jacobian
    LibmeshPetscCallQ(TaoSetJacobianInequalityRoutine(
        _tao, _gradient_i, _gradient_i, inequalityGradientFunctionWrapper, this));
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}
 
PetscErrorCode
OptimizeSolve::taoALDestroy()
{
  PetscFunctionBegin;
  if (_obj_function->getNumEqCons())
  {
    LibmeshPetscCallQ(VecDestroy(&_ce));
    LibmeshPetscCallQ(MatDestroy(&_gradient_e));
  }
  if (_obj_function->getNumInEqCons())
  {
    LibmeshPetscCallQ(VecDestroy(&_ci));
    LibmeshPetscCallQ(MatDestroy(&_gradient_i));
  }
 
  PetscFunctionReturn(PETSC_SUCCESS);
}