MadNLP Options

• MadNLP Options
• • Primary options
  • General options
  • Output options
  • Termination options
  • NLP options
  • Initialization Options
  • Hessian perturbation options
  • Restoration options
  • Line-search options
  • Barrier options
  • Linear Solver Options
  • • Iterator Options
  • Reference

Primary options

These options are used to set the values for other options. The default values are inferred from the NLP model.

• tol::Float64
  Termination tolerance. The default value is 1e-8 for double precision. The solver terminates if the scaled primal, dual, complementary infeasibility is less than tol. Valid range is $(0,\infty)$.
• callback::Type Valid values are: MadNLP.{DenseCallback,SparseCallback}.
• kkt_system::Type The type of KKT system. Valid values are MadNLP.{SpasreKKTSystem,SparseUnreducedKKTSystem,SparseCondensedKKTSystem,DenseKKTSystem,DenseCondensedKKTSystem}.
• linear_solver::Type
  Linear solver used for solving primal-dual system. Valid values are: {MadNLP.UmfpackSolver,MadNLP.LDLSolver,MadNLP.CHOLMODSolver, MadNLP.MumpsSolver, MadNLP.PardisoSolver, MadNLP.PardisoMKLSolver, MadNLP.Ma27Solver, MadNLP.Ma57Solver, MadNLP.Ma77Solver, MadNLP.Ma86Solver, MadNLP.Ma97Solver, MadNLP.LapackCPUSolver, MadNLPGPU.LapackGPUSolver,MadNLPGPU.RFSolver,MadNLPGPU.GLUSolver,MadNLPGPU.CuCholeskySolver,MadNLPGPU.CUDSSSolver} (some may require using extension packages). The selected solver should be properly built in the build procedure. See README.md file.

General options

• iterator::Type = RichardsonIterator
  Iterator used for iterative refinement. Valid values are: {MadNLPRichardson,MadNLPKrylov}.
  • Richardson uses Richardson iteration
  • Krylov uses restarted Generalized Minimal Residual method implemented in IterativeSolvers.jl.
• blas_num_threads::Int = 1
  Number of threads used for BLAS routines. Valid range is $[1,\infty)$.
• disable_garbage_collector::Bool = false
  If true, Julia garbage collector is temporarily disabled while solving the problem, and then enabled back once the solution is complete.
• rethrow_error::Bool = true
  If false, any internal error thrown by MadNLP and interruption exception (triggered by the user via ^C) is caught, and not rethrown. If an error is caught, the solver terminates with an error message.

Output options

• print_level::LogLevels = INFO
stdout print level. Any message with level less than print_level is not printed on stdout. Valid values are: MadNLP.{TRACE, DEBUG, INFO, NOTICE, WARN, ERROR}.
• output_file::String = INFO
  If not "", the output log is teed to the file at the path specified in output_file.
• file_print_level::LogLevels = TRACE
  File print level; any message with level less than file_print_level is not printed on the file specified in output_file. Valid values are: MadNLP.{TRACE, DEBUG, INFO, NOTICE, WARN, ERROR}.

Termination options

• max_iter::Int = 3000
  Maximum number of interior point iterations. The solver terminates with exit symbol :Maximum_Iterations_Exceeded if the interior point iteration count exceeds max_iter.
• acceptable_tol::Float64 = 1e-6
  Acceptable tolerance. The solver terminates if the scaled primal, dual, complementary infeasibility is less than acceptable_tol, for acceptable_iter consecutive interior point iteration steps.
• acceptable_iter::Int = 15
  Acceptable iteration tolerance. Valid rage is $[1,\infty)$.
• diverging_iterates_tol::Float64 = 1e20
  Diverging iteration tolerance. The solver terminates with exit symbol :Diverging_Iterates if the NLP error is greater than diverging_iterates_tol.
• max_wall_time::Float64 = 1e6
  Maximum wall time for interior point solver. The solver terminates with exit symbol :Maximum_WallTime_Exceeded if the total solver wall time exceeds max_wall_time.
• s_max::Float64 = 100.

NLP options

• kappa_d::Float64 = 1e-5
• fixed_variable_treatment::FixedVariableTreatments = MakeParameter
  Valid values are: MadNLP.{RelaxBound,MakeParameter}.
• equality_treatment::FixedVariableTreatments = MakeParameter
  Valid values are: MadNLP.{RelaxEquality,EnforceEquality}.
• jacobian_constant::Bool = false
  If true, constraint Jacobian is only evaluated once and reused.
• hessian_constant::Bool = false
  If true, Lagrangian Hessian is only evaluated once and reused.
• bound_push::Float64 = 1e-2
• bound_fac::Float64 = 1e-2
• hessian_approximation::Type = ExactHessian
• quasi_newton_options::QuasiNewtonOptions = QuasiNewtonOptions()
• inertia_correction_method::InertiaCorrectionMethods = INERTIA_AUTO
  Valid values are: MadNLP.{INERTIA_AUTO,INERTIA_BASED, INERTIA_FREE}.
  • INERTIA_BASED uses the strategy in Ipopt.
  • INERTIA_FREE uses the strategy in Chiang (2016).
  • INERTIA_AUTO uses INERTIA_BASED if inertia information is available and uses INERTIA_FREE otherwise.
• inertia_free_tol::Float64 = 0.

Initialization Options

dual_initialized::Bool = false
dual_initialization_method::Type = kkt_system <: MadNLP.SparseCondensedKKTSystem ? DualInitializeSetZero : DualInitializeLeastSquares

• constr_mult_init_max::Float64 = 1e3
• nlp_scaling::Bool = true:
  If true, MadNLP scales the nonlinear problem during the resolution.
• nlp_scaling_max_gradient::Float64 = 100.

Hessian perturbation options

• min_hessian_perturbation::Float64 = 1e-20
• first_hessian_perturbation::Float64 = 1e-4
• max_hessian_perturbation::Float64 = 1e20
• perturb_inc_fact_first::Float64 = 1e2
• perturb_inc_fact::Float64 = 8.
• perturb_dec_fact::Float64 = 1/3
• jacobian_regularization_exponent::Float64 = 1/4
• jacobian_regularization_value::Float64 = 1e-8

Restoration options

• soft_resto_pderror_reduction_factor::Float64 = 0.9999
• required_infeasibility_reduction::Float64 = 0.9

Line-search options

• obj_max_inc::Float64 = 5.
• kappha_soc::Float64 = 0.99
• max_soc::Int = 4
• alpha_min_frac::Float64 = 0.05
• s_theta::Float64 = 1.1
• s_phi::Float64 = 2.3
• eta_phi::Float64 = 1e-4
• kappa_soc::Float64 = 0.99
• gamma_theta::Float64 = 1e-5
• gamma_phi::Float64 = 1e-5
• delta::Float64 = 1
• kappa_sigma::Float64 = 1e10
• barrier_tol_factor::Float64 = 10.
• rho::Float64 = 1000.

Barrier options

• mu_init::Float64 = 1e-1
• mu_min::Float64 = 1e-9
• mu_superlinear_decrease_power::Float64 = 1.5
• tau_min::Float64 = 0.99
• mu_linear_decrease_factor::Float64 = .2

Linear Solver Options

Linear solver options are specific to the linear solver chosen at linear_solver option. Irrelevant options are ignored and a warning message is printed.

Ma27 (requires MadNLPHSL)

• ma27_pivtol::Float64 = 1e-8
• ma27_pivtolmax::Float64 = 1e-4
• ma27_liw_init_factor::Float64 = 5.
• ma27_la_init_factor::Float64 = 5.
• ma27_meminc_factor::Float64 = 2.

Ma57 (requires MadNLPHSL)

• ma57_pivtol::Float64 = 1e-8
• ma57_pivtolmax::Float64 = 1e-4
• ma57_pre_alloc::Float64 = 1.05
• ma57_pivot_order::Int = 5
• ma57_automatic_scaling::Bool = false
• ma57_block_size::Int = 16
• ma57_node_amalgamation::Int = 16
• ma57_small_pivot_flag::Int = 0

Ma77 (requires MadNLPHSL)

• ma77_buffer_lpage::Int = 4096
• ma77_buffer_npage::Int = 1600
• ma77_file_size::Int = 2097152
• ma77_maxstore::Int = 0
• ma77_nemin::Int = 8
• ma77_order::Ma77.Ordering = Ma77.METIS
• ma77_print_level::Int = -1
• ma77_small::Float64 = 1e-20
• ma77_static::Float64 = 0.
• ma77_u::Float64 = 1e-8
• ma77_umax::Float64 = 1e-4

Ma86 (requires MadNLPHSL)

• ma86_num_threads::Int = 1
• ma86_print_level::Float64 = -1
• ma86_nemin::Int = 32
• ma86_order::Ma86.Ordering = Ma86.METIS
• ma86_scaling::Ma86.Scaling = Ma86.SCALING_NONE
• ma86_small::Float64 = 1e-20
• ma86_static::Float64 = 0.
• ma86_u::Float64 = 1e-8
• ma86_umax::Float64 = 1e-4

Ma97 (requires MadNLPHSL)

• ma97_num_threads::Int = 1
• ma97_print_level::Int = -1
• ma97_nemin::Int = 8
• ma97_order::Ma97.Ordering = Ma97.METIS
• ma97_scaling::Ma97.Scaling = Ma97.SCALING_NONE
• ma97_small::Float64 = 1e-20
• ma97_u::Float64 = 1e-8
• ma97_umax::Float64 = 1e-4

Mumps (requires MadNLPMumps)

• mumps_dep_tol::Float64 = 0.
• mumps_mem_percent::Int = 1000
• mumps_permuting_scaling::Int = 7
• mumps_pivot_order::Int = 7
• mumps_pivtol::Float64 = 1e-6
• mumps_pivtolmax::Float64 = .1
• mumps_scaling::Int = 77

Umfpack (requires MadNLPUmfpack)

• umfpack_pivtol::Float64 = 1e-4
• umfpack_pivtolmax::Float64 = 1e-1
• umfpack_sym_pivtol::Float64 = 1e-3
• umfpack_block_size::Float64 = 16
• umfpack_strategy::Float64 = 2.

Pardiso (requires MadNLPPardiso)

• pardiso_matching_strategy::Pardiso.MatchingStrategy = COMPLETE2x2
• pardiso_max_inner_refinement_steps::Int = 1
• pardiso_msglvl::Int = 0
• pardiso_order::Int = 2

PardisoMKL

• pardisomkl_num_threads::Int = 1
• pardiso_matching_strategy::PardisoMKL.MatchingStrategy = COMPLETE2x2
• pardisomkl_max_iterative_refinement_steps::Int = 1
• pardisomkl_msglvl::Int = 0
• pardisomkl_order::Int = 2

LapackGPU (requires MadNLPGPU)

• lapackgpu_algorithm::LapackGPU.Algorithms = BUNCHKAUFMAN

LapackCPU

• lapackcpu_algorithm::LapackCPU.Algorithms = BUNCHKAUFMAN

Iterator Options

Richardson

• richardson_max_iter::Int = 10
  Maximum number of Richardson iteration steps. Valid range is $[1,\infty)$.
• richardson_tol::Float64 = 1e-10
  Convergence tolerance of Richardson iteration. Valid range is $(0,\infty)$.
• richardson_acceptable_tol::Float64 = 1e-5
  Acceptable convergence tolerance of Richardson iteration. If the Richardson iteration counter exceeds richardson_max_iter without satisfying the convergence criteria set with richardson_tol, the Richardson solver checks whether the acceptable convergence criteria set with richardson_acceptable_tol is satisfied; if the acceptable convergence criteria is satisfied, the computed step is used; otherwise, the augmented system is treated to be singular. Valid range is $(0,\infty)$.

Krylov (requires MadNLPIterative)

• krylov_max_iter::Int = 10
  Maximum number of Krylov iteration steps. Valid range is $[1,\infty)$.
• krylov_tol::Float64 = 1e-10
  Convergence tolerance of Krylov iteration. Valid range is $(0,\infty)$.
• krylov_acceptable_tol::Float64 = 1e-5
  Acceptable convergence tolerance of Krylov iteration. If the Krylov iteration counter exceeds krylov_max_iter without satisfying the convergence criteria set with krylov_tol, the Krylov solver checks whether the acceptable convergence criteria set with krylov_acceptable_tol is satisfied; if the acceptable convergence criteria is satisfied, the computed step is used; otherwise, the augmented system is treated to be singular. Valid range is $(0,\infty)$.
• krylov_restart::Int = 5
  Maximum Krylov iteration before restarting. Valid range is $[1,\infty)$.

Reference

[Bunch, 1977]: J R Bunch and L Kaufman, Some stable methods for calculating inertia and solving symmetric linear systems, Mathematics of Computation 31:137 (1977), 163-179.

[Greif, 2014]: Greif, Chen, Erin Moulding, and Dominique Orban. "Bounds on eigenvalues of matrices arising from interior-point methods." SIAM Journal on Optimization 24.1 (2014): 49-83.

[Wächter, 2006]: Wächter, Andreas, and Lorenz T. Biegler. "On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming." Mathematical programming 106.1 (2006): 25-57.

[Chiang, 2016]: Chiang, Nai-Yuan, and Victor M. Zavala. "An inertia-free filter line-search algorithm for large-scale nonlinear programming." Computational Optimization and Applications 64.2 (2016): 327-354.