optimization_ex2.C File Reference

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Classes
class	AssembleOptimization
	This class encapsulate all functionality required for assembling the objective function, gradient, and hessian. More...

Functions
int	main (int argc, char **argv)

Function Documentation

main()

int main	(	int	argc,
		char **	argv
	)

Definition at line 396 of file optimization_ex2.C.

{
  LibMeshInit init (argc, argv);
 
#ifndef LIBMESH_HAVE_PETSC_TAO
 
  libmesh_example_requires(false, "PETSc >= 3.5.0 with built-in TAO support");
 
#elif LIBMESH_USE_COMPLEX_NUMBERS
 
  // According to
  // http://www.mcs.anl.gov/research/projects/tao/documentation/installation.html
  // TAO & PETSc-complex are currently mutually exclusive
  libmesh_example_requires(false, "PETSc >= 3.5.0 with built-in TAO support & real-numbers only");
 
#endif
 
  // We use a 2D domain.
  libmesh_example_requires(LIBMESH_DIM > 1, "--disable-1D-only");
 
  // TAO is giving us problems in parallel?
  if (init.comm().size() != 1)
    {
      libMesh::out << "This example can currently only be run in serial." << std::endl;
      return 77;
    }
 
  GetPot infile("optimization_ex2.in");
  const std::string approx_order = infile("approx_order", "FIRST");
  const std::string fe_family = infile("fe_family", "LAGRANGE");
  const unsigned int n_elem = infile("n_elem", 10);
 
  Mesh mesh(init.comm());
  MeshTools::Generation::build_square (mesh,
                                       n_elem,
                                       n_elem,
                                       -1., 1.,
                                       -1., 1.,
                                       QUAD9);
 
  mesh.print_info();
 
  EquationSystems equation_systems (mesh);
 
  OptimizationSystem & system =
    equation_systems.add_system<OptimizationSystem> ("Optimization");
 
  // The default is to use PETSc/Tao solvers, but let the user change
  // the optimization solver package on the fly.
  {
    const std::string optimization_solver_type = infile("optimization_solver_type",
                                                        "PETSC_SOLVERS");
    SolverPackage sp = Utility::string_to_enum<SolverPackage>(optimization_solver_type);
    std::unique_ptr<OptimizationSolver<Number>> new_solver =
      OptimizationSolver<Number>::build(system, sp);
    system.optimization_solver.reset(new_solver.release());
  }
 
  // Set tolerances and maximum iteration counts directly on the optimization solver.
  system.optimization_solver->max_objective_function_evaluations = 128;
  system.optimization_solver->objective_function_relative_tolerance = 1.e-4;
  system.optimization_solver->verbose = true;
 
  AssembleOptimization assemble_opt(system);
 
  system.add_variable("u",
                      Utility::string_to_enum<Order>   (approx_order),
                      Utility::string_to_enum<FEFamily>(fe_family));
 
  system.optimization_solver->objective_object = &assemble_opt;
  system.optimization_solver->gradient_object = &assemble_opt;
  system.optimization_solver->hessian_object = &assemble_opt;
  system.optimization_solver->equality_constraints_object = &assemble_opt;
  system.optimization_solver->equality_constraints_jacobian_object = &assemble_opt;
  system.optimization_solver->inequality_constraints_object = &assemble_opt;
  system.optimization_solver->inequality_constraints_jacobian_object = &assemble_opt;
  system.optimization_solver->lower_and_upper_bounds_object = &assemble_opt;
 
  // system.matrix and system.rhs are used for the gradient and Hessian,
  // so in this case we add an extra matrix and vector to store A and F.
  // This makes it easy to write the code for evaluating the objective,
  // gradient, and hessian.
  system.add_matrix("A_matrix");
  system.add_vector("F_vector");
  assemble_opt.A_matrix = &system.get_matrix("A_matrix");
  assemble_opt.F_vector = &system.get_vector("F_vector");
 
 
  equation_systems.init();
  equation_systems.print_info();
 
  assemble_opt.assemble_A_and_F();
 
  {
    std::vector<std::set<numeric_index_type>> constraint_jac_sparsity;
    std::set<numeric_index_type> sparsity_row;
    sparsity_row.insert(17);
    constraint_jac_sparsity.push_back(sparsity_row);
    sparsity_row.clear();
 
    sparsity_row.insert(23);
    constraint_jac_sparsity.push_back(sparsity_row);
    sparsity_row.clear();
 
    sparsity_row.insert(98);
    sparsity_row.insert(185);
    constraint_jac_sparsity.push_back(sparsity_row);
 
    system.initialize_equality_constraints_storage(constraint_jac_sparsity);
  }
 
  {
    std::vector<std::set<numeric_index_type>> constraint_jac_sparsity;
    std::set<numeric_index_type> sparsity_row;
    sparsity_row.insert(200);
    sparsity_row.insert(201);
    constraint_jac_sparsity.push_back(sparsity_row);
 
    system.initialize_inequality_constraints_storage(constraint_jac_sparsity);
  }
 
  // We need to close the matrix so that we can use it to store the
  // Hessian during the solve.
  system.matrix->close();
  system.solve();
 
  // Print convergence information
  system.optimization_solver->print_converged_reason();
 
  // Write the solution to file if the optimization solver converged
  if (system.optimization_solver->get_converged_reason() > 0)
    {
      std::stringstream filename;
      ExodusII_IO (mesh).write_equation_systems("optimization_soln.exo",
                                                equation_systems);
    }
 
  return 0;
}

References AssembleOptimization::A_matrix, libMesh::ImplicitSystem::add_matrix(), libMesh::EquationSystems::add_system(), libMesh::System::add_variable(), libMesh::System::add_vector(), AssembleOptimization::assemble_A_and_F(), libMesh::MeshTools::Generation::build_square(), libMesh::SparseMatrix< T >::close(), AssembleOptimization::F_vector, libMesh::ImplicitSystem::get_matrix(), libMesh::System::get_vector(), libMesh::TriangleWrapper::init(), libMesh::EquationSystems::init(), libMesh::OptimizationSystem::initialize_equality_constraints_storage(), libMesh::OptimizationSystem::initialize_inequality_constraints_storage(), libMesh::ImplicitSystem::matrix, mesh, libMesh::MeshTools::n_elem(), libMesh::OptimizationSystem::optimization_solver, libMesh::out, libMesh::EquationSystems::print_info(), libMesh::MeshBase::print_info(), libMesh::QUAD9, libMesh::OptimizationSystem::solve(), and libMesh::MeshOutput< MT >::write_equation_systems().