Optimization algorithms

Warning

Some capabilities may require the installation of GEMSEO with all its features and some others may depend on plugins.

Warning

All the features of the wrapped libraries may not be exposed through GEMSEO.

Note

The algorithm settings can be passed to a function of the form

function(..., settings_model: Base | None = None, **settings: Any)

either one by one:

function(..., setting_name_1=setting_name_1, setting_name_2=setting_name_2, ...)

or using the argument name "settings" and the Pydantic model associated with the algorithm:

settings = AlgorithmSettings(setting_name_1=setting_name_1, setting_name_2=setting_name_2, ...)
function(..., settings_model=settings)

Algorithm ▲▼	Library ▲▼	Name in GEMSEO ▲▼	Package ▲▼	Handle equality constraints ▲▼	Handle inequality constraints ▲▼	Handle float variables ▲▼	Handle integer variables ▲▼	Handle multi-objective ▲▼	Require gradient ▲▼
Augmented_Lagrangian_order_0		Augmented_Lagrangian_order_0	gemseo	✓	✓	✓	✗	✗	✗
Augmented_Lagrangian_order_1		Augmented_Lagrangian_order_1	gemseo	✓	✓	✓	✗	✗	✓
Differential evolution	SciPy Global Optimization	DIFFERENTIAL_EVOLUTION	gemseo	✓	✓	✓	✓	✗	✗
Dual annealing	SciPy Global Optimization	DUAL_ANNEALING	gemseo	✗	✗	✓	✓	✗	✗
Dual simplex	SciPy Linear Programming	DUAL_SIMPLEX	gemseo	✓	✓	✓	✗	✗	✗
Interior point method	SciPy Linear Programming	INTERIOR_POINT	gemseo	✓	✓	✓	✗	✗	✗
L-BFGS-B	SciPy Local	L-BFGS-B	gemseo	✗	✗	✓	✗	✗	✓
mNBI	MNBI	MNBI	gemseo	✓	✓	✓	✓	✓	✗
Multi-start optimization		MultiStart	gemseo	✓	✓	✓	✓	✓	✗
NELDER-MEAD	SciPy Local	NELDER-MEAD	gemseo	✗	✗	✓	✗	✗	✗
BFGS	NLopt	NLOPT_BFGS	gemseo	✗	✗	✓	✗	✗	✓
BOBYQA	NLopt	NLOPT_BOBYQA	gemseo	✗	✗	✓	✗	✗	✗
COBYLA	NLopt	NLOPT_COBYLA	gemseo	✓	✓	✓	✗	✗	✗
MMA	NLopt	NLOPT_MMA	gemseo	✗	✓	✓	✗	✗	✓
NEWUOA	NLopt	NLOPT_NEWUOA	gemseo	✗	✗	✓	✗	✗	✗
SLSQP	NLopt	NLOPT_SLSQP	gemseo	✓	✓	✓	✗	✗	✓
SHGO	SciPy Global Optimization	SHGO	gemseo	✓	✓	✓	✓	✗	✗
SLSQP	SciPy Local	SLSQP	gemseo	✓	✓	✓	✗	✗	✓
Branch & Cut algorithm	SciPy Mixed-Integer Linear Programming	Scipy_MILP	gemseo	✓	✓	✓	✓	✗	✗
TNC	SciPy Local	TNC	gemseo	✗	✗	✓	✗	✗	✓

Augmented_Lagrangian_order_0

Module: gemseo.algos.opt.augmented_lagrangian.augmented_lagrangian_order_0

from gemseo.settings.opt import Augmented_Lagrangian_order_0_Settings

Augmented Lagrangian algorithm for gradient-less functions.

Required settings

• sub_algorithm_name : <class 'str'>

  The name of the optimizer used to solve each sub-problem.

Optional settings

• enable_progress_bar : typing.Optional[bool], optional

  Whether to enable the progress bar in the optimization log.

  If None, use the global value of enable_progress_bar (see the configure function to change it globally).

  By default it is set to None.

• eq_tolerance : <class 'float'>, optional

  The tolerance on the equality constraints.

  By default it is set to 0.01.

• ftol_abs : <class 'float'>, optional

  The absolute tolerance on the objective function.

  By default it is set to 1e-09.

• ftol_rel : <class 'float'>, optional

  The relative tolerance on the objective function.

  By default it is set to 1e-09.

• gamma : <class 'float'>, optional

  The penalty increase factor.

  By default it is set to 1.5.

• ineq_tolerance : <class 'float'>, optional

  The tolerance on the inequality constraints.

  By default it is set to 0.0001.

• initial_rho : <class 'float'>, optional

  The initial penalty value.

  By default it is set to 10.0.

• log_problem : <class 'bool'>, optional

  Whether to log the definition and result of the problem.

  By default it is set to True.

• max_iter : <class 'int'>, optional

  The maximum number of iterations.

  By default it is set to 1000.

• max_rho : <class 'float'>, optional

  The maximum penalty value.

  By default it is set to 10000.

• max_time : <class 'float'>, optional

  The maximum runtime in seconds, disabled if 0.

  By default it is set to 0.0.

• normalize_design_space : <class 'bool'>, optional

  Whether to normalize the design space variables between 0 and 1.

  By default it is set to True.

• reset_iteration_counters : <class 'bool'>, optional

  Whether to reset the iteration counters before each execution.

  By default it is set to True.

• round_ints : <class 'bool'>, optional

  Whether to round the integer variables.

  By default it is set to True.

• scaling_threshold : typing.Optional[typing.Annotated[float, Ge(ge=0)]], optional

  The threshold on the reference function value that triggers scaling.

  If None, do not scale the functions.

  By default it is set to None.

• stop_crit_n_x : <class 'int'>, optional

  The minimum number of design vectors to consider in the stopping criteria.

  By default it is set to 3.

• store_jacobian : <class 'bool'>, optional

  Whether to store the Jacobian matrices in the database.

  This argument is ignored when the use_database option is False. If a gradient-based algorithm is used, this option cannot be set along with kkt options.

  By default it is set to True.

• sub_algorithm_settings : collections.abc.Mapping[str, typing.Any], optional

  The settings of the optimizer used to solve each sub-problem.

  By default it is set to {}.

• sub_problem_constraints : collections.abc.Iterable[str], optional

  The constraints to keep in the sub-problem.

  If empty, all constraints are handled by the Augmented Lagrangian method which implies that the sub-problem is unconstrained.

  By default it is set to ().

• tau : <class 'float'>, optional

  The threshold to increase the penalty.

  By default it is set to 0.9.

• update_options_callback : typing.Optional[typing.Annotated[typing.Callable[[typing.Any], typing.Any], WithJsonSchema(json_schema={}, mode=None)]], optional

  A callable for updating parameters or a function call.

  By default it is set to None.

• use_database : <class 'bool'>, optional

  Whether to wrap the functions in the database.

  By default it is set to True.

• use_one_line_progress_bar : <class 'bool'>, optional

  Whether to log the progress bar on a single line.

  By default it is set to False.

• xtol_abs : <class 'float'>, optional

  The absolute tolerance on the design parameters.

  By default it is set to 1e-09.

• xtol_rel : <class 'float'>, optional

  The relative tolerance on the design parameters.

  By default it is set to 1e-09.

Augmented_Lagrangian_order_1

Module: gemseo.algos.opt.augmented_lagrangian.augmented_lagrangian_order_1

from gemseo.settings.opt import Augmented_Lagrangian_order_1_Settings

Augmented Lagrangian algorithm using gradient information

Required settings

• sub_algorithm_name : <class 'str'>

  The name of the optimizer used to solve each sub-problem.

Optional settings

• enable_progress_bar : typing.Optional[bool], optional

  Whether to enable the progress bar in the optimization log.

  If None, use the global value of enable_progress_bar (see the configure function to change it globally).

  By default it is set to None.

• eq_tolerance : <class 'float'>, optional

  The tolerance on the equality constraints.

  By default it is set to 0.01.

• ftol_abs : <class 'float'>, optional

  The absolute tolerance on the objective function.

  By default it is set to 1e-09.

• ftol_rel : <class 'float'>, optional

  The relative tolerance on the objective function.

  By default it is set to 1e-09.

• gamma : <class 'float'>, optional

  The penalty increase factor.

  By default it is set to 1.5.

• ineq_tolerance : <class 'float'>, optional

  The tolerance on the inequality constraints.

  By default it is set to 0.0001.

• initial_rho : <class 'float'>, optional

  The initial penalty value.

  By default it is set to 10.0.

• kkt_tol_abs : <class 'float'>, optional

  The absolute tolerance on the KKT residual norm.

  If inf this criterion is not activated.

  By default it is set to inf.

• kkt_tol_rel : <class 'float'>, optional

  The relative tolerance on the KKT residual norm.

  If inf this criterion is not activated.

  By default it is set to inf.

• log_problem : <class 'bool'>, optional

  Whether to log the definition and result of the problem.

  By default it is set to True.

• max_iter : <class 'int'>, optional

  The maximum number of iterations.

  By default it is set to 1000.

• max_rho : <class 'float'>, optional

  The maximum penalty value.

  By default it is set to 10000.

• max_time : <class 'float'>, optional

  The maximum runtime in seconds, disabled if 0.

  By default it is set to 0.0.

• normalize_design_space : <class 'bool'>, optional

  Whether to normalize the design space variables between 0 and 1.

  By default it is set to True.

• reset_iteration_counters : <class 'bool'>, optional

  Whether to reset the iteration counters before each execution.

  By default it is set to True.

• round_ints : <class 'bool'>, optional

  Whether to round the integer variables.

  By default it is set to True.

• scaling_threshold : typing.Optional[typing.Annotated[float, Ge(ge=0)]], optional

  The threshold on the reference function value that triggers scaling.

  If None, do not scale the functions.

  By default it is set to None.

• stop_crit_n_x : <class 'int'>, optional

  The minimum number of design vectors to consider in the stopping criteria.

  By default it is set to 3.

• store_jacobian : <class 'bool'>, optional

  Whether to store the Jacobian matrices in the database.

  This argument is ignored when the use_database option is False. If a gradient-based algorithm is used, this option cannot be set along with kkt options.

  By default it is set to True.

• sub_algorithm_settings : collections.abc.Mapping[str, typing.Any], optional

  The settings of the optimizer used to solve each sub-problem.

  By default it is set to {}.

• sub_problem_constraints : collections.abc.Iterable[str], optional

  The constraints to keep in the sub-problem.

  If empty, all constraints are handled by the Augmented Lagrangian method which implies that the sub-problem is unconstrained.

  By default it is set to ().

• tau : <class 'float'>, optional

  The threshold to increase the penalty.

  By default it is set to 0.9.

• update_options_callback : typing.Optional[typing.Annotated[typing.Callable[[typing.Any], typing.Any], WithJsonSchema(json_schema={}, mode=None)]], optional

  A callable for updating parameters or a function call.

  By default it is set to None.

• use_database : <class 'bool'>, optional

  Whether to wrap the functions in the database.

  By default it is set to True.

• use_one_line_progress_bar : <class 'bool'>, optional

  Whether to log the progress bar on a single line.

  By default it is set to False.

• xtol_abs : <class 'float'>, optional

  The absolute tolerance on the design parameters.

  By default it is set to 1e-09.

• xtol_rel : <class 'float'>, optional

  The relative tolerance on the design parameters.

  By default it is set to 1e-09.

DIFFERENTIAL_EVOLUTION

Module: gemseo.algos.opt.scipy_global.scipy_global

from gemseo.settings.opt import DIFFERENTIAL_EVOLUTION_Settings

Differential Evolution algorithm

More details about the algorithm and its settings on https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.differential_evolution.html.

Optional settings

• atol : <class 'float'>, optional

  The absolute tolerance for convergence.

  By default it is set to 0.0.

• disp : <class 'bool'>, optional

  Whether to print convergence messages.

  By default it is set to False.

• enable_progress_bar : typing.Optional[bool], optional

  Whether to enable the progress bar in the optimization log.

  If None, use the global value of enable_progress_bar (see the configure function to change it globally).

  By default it is set to None.

• eq_tolerance : <class 'float'>, optional

  The tolerance on the equality constraints.

  By default it is set to 1e-06.

• ftol_abs : <class 'float'>, optional

  The absolute tolerance on the objective function.

  By default it is set to 1e-09.

• ftol_rel : <class 'float'>, optional

  The relative tolerance on the objective function.

  By default it is set to 1e-09.

• ineq_tolerance : <class 'float'>, optional

  The tolerance on the inequality constraints.

  By default it is set to 0.0001.

• init : typing.Union[str, gemseo.utils.pydantic_ndarray._NDArrayPydantic[typing.Any, numpy.dtype[float]]], optional

  The method to perform the population initialization as a string

  or the initial population as an array.

  By default it is set to latinhypercube.

• log_problem : <class 'bool'>, optional

  Whether to log the definition and result of the problem.

  By default it is set to True.

• max_iter : <class 'int'>, optional

  The maximum number of iterations.

  By default it is set to 9223372036854775807.

• max_time : <class 'float'>, optional

  The maximum runtime in seconds, disabled if 0.

  By default it is set to 0.0.

• mutation : typing.Union[float, tuple[float, float]], optional

  The mutation constant.

  If specified as a float it should be in the range [0, 2]. If specified as a tuple(min, max) dithering is employed.

  By default it is set to (0.5, 1.0).

• normalize_design_space : <class 'bool'>, optional

  Whether to normalize the design space variables between 0 and 1.

  By default it is set to True.

• polish : <class 'bool'>, optional

  Whether to polish the best population member at the end.

  By default it is set to True.

• popsize : <class 'int'>, optional

  The multiplier for setting the total population size.

  By default it is set to 15.

• recombination : <class 'float'>, optional

  The recombination constant.

  By default it is set to 0.7.

• reset_iteration_counters : <class 'bool'>, optional

  Whether to reset the iteration counters before each execution.

  By default it is set to True.

• round_ints : <class 'bool'>, optional

  Whether to round the integer variables.

  By default it is set to True.

• scaling_threshold : typing.Optional[typing.Annotated[float, Ge(ge=0)]], optional

  The threshold on the reference function value that triggers scaling.

  If None, do not scale the functions.

  By default it is set to None.

• seed : <class 'int'>, optional

  The random seed.

  By default it is set to 0.

• stop_crit_n_x : <class 'int'>, optional

  The minimum number of design vectors to consider in the stopping criteria.

  By default it is set to 3.

• store_jacobian : <class 'bool'>, optional

  Whether to store the Jacobian matrices in the database.

  This argument is ignored when the use_database option is False. If a gradient-based algorithm is used, this option cannot be set along with kkt options.

  By default it is set to True.

• strategy : <class 'str'>, optional

  The differential evolution strategy to use.

  By default it is set to best1bin.

• tol : <class 'float'>, optional

  The relative tolerance for convergence.

  By default it is set to 0.01.

• updating : <class 'str'>, optional

  The best solution vector updating strategy.

  By default it is set to immediate.

• use_database : <class 'bool'>, optional

  Whether to wrap the functions in the database.

  By default it is set to True.

• use_one_line_progress_bar : <class 'bool'>, optional

  Whether to log the progress bar on a single line.

  By default it is set to False.

• workers : <class 'int'>, optional

  The number of parallel workers the population is subdivided in.

  By default it is set to 1.

• xtol_abs : <class 'float'>, optional

  The absolute tolerance on the design parameters.

  By default it is set to 1e-09.

• xtol_rel : <class 'float'>, optional

  The relative tolerance on the design parameters.

  By default it is set to 1e-09.

DUAL_ANNEALING

Module: gemseo.algos.opt.scipy_global.scipy_global

from gemseo.settings.opt import DUAL_ANNEALING_Settings

Dual annealing

More details about the algorithm and its settings on https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.dual_annealing.html.

Optional settings

• accept : <class 'float'>, optional

  The acceptance distribution parameter.

  The lower the acceptance parameter, the smaller the probability of acceptance.

  By default it is set to -5.

• enable_progress_bar : typing.Optional[bool], optional

  Whether to enable the progress bar in the optimization log.

  If None, use the global value of enable_progress_bar (see the configure function to change it globally).

  By default it is set to None.

• eq_tolerance : <class 'float'>, optional

  The tolerance on the equality constraints.

  By default it is set to 1e-06.

• ftol_abs : <class 'float'>, optional

  The absolute tolerance on the objective function.

  By default it is set to 1e-09.

• ftol_rel : <class 'float'>, optional

  The relative tolerance on the objective function.

  By default it is set to 1e-09.

• ineq_tolerance : <class 'float'>, optional

  The tolerance on the inequality constraints.

  By default it is set to 0.0001.

• initial_temp : <class 'float'>, optional

  The initial temperature.

  Use higher values to facilitates a wider search of the energy landscape.

  By default it is set to 5230.

• log_problem : <class 'bool'>, optional

  Whether to log the definition and result of the problem.

  By default it is set to True.

• max_iter : <class 'int'>, optional

  The maximum number of iterations.

  By default it is set to 9223372036854775807.

• max_time : <class 'float'>, optional

  The maximum runtime in seconds, disabled if 0.

  By default it is set to 0.0.

• no_local_search : <class 'bool'>, optional

  Whether to perform local search.

  By default it is set to False.

• normalize_design_space : <class 'bool'>, optional

  Whether to normalize the design space variables between 0 and 1.

  By default it is set to True.

• reset_iteration_counters : <class 'bool'>, optional

  Whether to reset the iteration counters before each execution.

  By default it is set to True.

• restart_temp_ratio : <class 'float'>, optional

  The temperature ratio under which the reannealing process is triggered.

  By default it is set to 2e-05.

• round_ints : <class 'bool'>, optional

  Whether to round the integer variables.

  By default it is set to True.

• scaling_threshold : typing.Optional[typing.Annotated[float, Ge(ge=0)]], optional

  The threshold on the reference function value that triggers scaling.

  If None, do not scale the functions.

  By default it is set to None.

• seed : <class 'int'>, optional

  The random seed.

  By default it is set to 0.

• stop_crit_n_x : <class 'int'>, optional

  The minimum number of design vectors to consider in the stopping criteria.

  By default it is set to 3.

• store_jacobian : <class 'bool'>, optional

  Whether to store the Jacobian matrices in the database.

  This argument is ignored when the use_database option is False. If a gradient-based algorithm is used, this option cannot be set along with kkt options.

  By default it is set to True.

• use_database : <class 'bool'>, optional

  Whether to wrap the functions in the database.

  By default it is set to True.

• use_one_line_progress_bar : <class 'bool'>, optional

  Whether to log the progress bar on a single line.

  By default it is set to False.

• visit : <class 'float'>, optional

  The visiting distribution parameter.

  Higher values give the visiting distribution a heavier tail, this makes the algorithm jump to a more distant region.

  By default it is set to 2.62.

• xtol_abs : <class 'float'>, optional

  The absolute tolerance on the design parameters.

  By default it is set to 1e-09.

• xtol_rel : <class 'float'>, optional

  The relative tolerance on the design parameters.

  By default it is set to 1e-09.

DUAL_SIMPLEX

Module: gemseo.algos.opt.scipy_linprog.scipy_linprog

from gemseo.settings.opt import DUAL_SIMPLEX_Settings

Linear programming using the HiGHS dual simplex solver.

More details about the algorithm and its settings on https://docs.scipy.org/doc/scipy/reference/optimize.linprog-highs-ds.html.

Optional settings

• autoscale : <class 'bool'>, optional

  Whether to perform auto-scaling of the constraints.

  By default it is set to False.

• disp : <class 'bool'>, optional

  Whether to print convergence messages.

  By default it is set to False.

• dual_feasibility_tolerance : <class 'float'>, optional

  The dual feasability tolerance.

  By default it is set to 1e-07.

• enable_progress_bar : typing.Optional[bool], optional

  Whether to enable the progress bar in the optimization log.

  If None, use the global value of enable_progress_bar (see the configure function to change it globally).

  By default it is set to None.

• eq_tolerance : <class 'float'>, optional

  The tolerance on the equality constraints.

  By default it is set to 0.01.

• ftol_abs : <class 'float'>, optional

  The absolute tolerance on the objective function.

  By default it is set to 0.0.

• ftol_rel : <class 'float'>, optional

  The relative tolerance on the objective function.

  By default it is set to 0.0.

• ineq_tolerance : <class 'float'>, optional

  The tolerance on the inequality constraints.

  By default it is set to 0.0001.

• log_problem : <class 'bool'>, optional

  Whether to log the definition and result of the problem.

  By default it is set to True.

• max_iter : <class 'int'>, optional

  The maximum number of iterations.

  By default it is set to 1000.

• max_time : <class 'float'>, optional

  The maximum runtime in seconds, disabled if 0.

  By default it is set to 0.0.

• normalize_design_space : <class 'bool'>, optional

  Whether to normalize the design space variables between 0 and 1.

  By default it is set to True.

• presolve : <class 'bool'>, optional

  Whether to perform a preliminary analysis on the problem before solving.

  It attempts to detect infeasibility, unboundedness or problem simplifications.

  By default it is set to True.

• primal_feasibility_tolerance : <class 'float'>, optional

  The primal feasability tolerance.

  By default it is set to 1e-07.

• reset_iteration_counters : <class 'bool'>, optional

  Whether to reset the iteration counters before each execution.

  By default it is set to True.

• round_ints : <class 'bool'>, optional

  Whether to round the integer variables.

  By default it is set to True.

• rr : <class 'bool'>, optional

  Whether to remove linearly dependent equality-constraints.

  By default it is set to True.

• rr_method : typing.Literal['SVD', 'pivot', 'ID', None], optional

  The method to remove redundancy, either 'SVD', 'pivot' or 'ID'.

  If None, use “SVD” if the matrix is nearly full rank. If not, uses “pivot”. The behavior of this default is subject to change without prior notice.

  By default it is set to None.

• scaling_threshold : typing.Optional[typing.Annotated[float, Ge(ge=0)]], optional

  The threshold on the reference function value that triggers scaling.

  If None, do not scale the functions.

  By default it is set to None.

• simplex_dual_edge_weight_strategy : <class 'str'>, optional

  Strategy for simplex dual edge weights.

  Available strategies: dantzig, devex, steepest and steepest-devex.

  By default it is set to steepest-devex.

• stop_crit_n_x : <class 'int'>, optional

  The minimum number of design vectors to consider in the stopping criteria.

  By default it is set to 3.

• store_jacobian : <class 'bool'>, optional

  Whether to store the Jacobian matrices in the database.

  This argument is ignored when the use_database option is False. If a gradient-based algorithm is used, this option cannot be set along with kkt options.

  By default it is set to True.

• use_database : <class 'bool'>, optional

  Whether to wrap the functions in the database.

  By default it is set to True.

• use_one_line_progress_bar : <class 'bool'>, optional

  Whether to log the progress bar on a single line.

  By default it is set to False.

• xtol_abs : <class 'float'>, optional

  The absolute tolerance on the design parameters.

  By default it is set to 0.0.

• xtol_rel : <class 'float'>, optional

  The relative tolerance on the design parameters.

  By default it is set to 0.0.

INTERIOR_POINT

Module: gemseo.algos.opt.scipy_linprog.scipy_linprog

from gemseo.settings.opt import INTERIOR_POINT_Settings

Linear programming using the HiGHS interior point solver.

More details about the algorithm and its settings on https://docs.scipy.org/doc/scipy/reference/optimize.linprog-highs-ipm.html.

Optional settings

• autoscale : <class 'bool'>, optional

  Whether to perform auto-scaling of the constraints.

  By default it is set to False.

• disp : <class 'bool'>, optional

  Whether to print convergence messages.

  By default it is set to False.

• dual_feasibility_tolerance : <class 'float'>, optional

  The tolerance on the feasibility of the dual problem.

  By default it is set to 1e-07.

• enable_progress_bar : typing.Optional[bool], optional

  Whether to enable the progress bar in the optimization log.

  If None, use the global value of enable_progress_bar (see the configure function to change it globally).

  By default it is set to None.

• eq_tolerance : <class 'float'>, optional

  The tolerance on the equality constraints.

  By default it is set to 0.01.

• ftol_abs : <class 'float'>, optional

  The absolute tolerance on the objective function.

  By default it is set to 0.0.

• ftol_rel : <class 'float'>, optional

  The relative tolerance on the objective function.

  By default it is set to 0.0.

• ineq_tolerance : <class 'float'>, optional

  The tolerance on the inequality constraints.

  By default it is set to 0.0001.

• ipm_optimality_tolerance : <class 'float'>, optional

  Optimality tolerance.

  By default it is set to 1e-08.

• log_problem : <class 'bool'>, optional

  Whether to log the definition and result of the problem.

  By default it is set to True.

• max_iter : <class 'int'>, optional

  The maximum number of iterations.

  By default it is set to 1000.

• max_time : <class 'float'>, optional

  The maximum runtime in seconds, disabled if 0.

  By default it is set to 0.0.

• normalize_design_space : <class 'bool'>, optional

  Whether to normalize the design space variables between 0 and 1.

  By default it is set to True.

• presolve : <class 'bool'>, optional

  Whether to perform a preliminary analysis on the problem before solving.

  It attempts to detect infeasibility, unboundedness or problem simplifications.

  By default it is set to True.

• primal_feasibility_tolerance : <class 'float'>, optional

  The tolerance on the feasibility of the primal problem.

  By default it is set to 1e-07.

• reset_iteration_counters : <class 'bool'>, optional

  Whether to reset the iteration counters before each execution.

  By default it is set to True.

• round_ints : <class 'bool'>, optional

  Whether to round the integer variables.

  By default it is set to True.

• rr : <class 'bool'>, optional

  Whether to remove linearly dependent equality-constraints.

  By default it is set to True.

• rr_method : typing.Literal['SVD', 'pivot', 'ID', None], optional

  The method to remove redundancy, either 'SVD', 'pivot' or 'ID'.

  If None, use “SVD” if the matrix is nearly full rank. If not, uses “pivot”. The behavior of this default is subject to change without prior notice.

  By default it is set to None.

• scaling_threshold : typing.Optional[typing.Annotated[float, Ge(ge=0)]], optional

  The threshold on the reference function value that triggers scaling.

  If None, do not scale the functions.

  By default it is set to None.

• stop_crit_n_x : <class 'int'>, optional

  The minimum number of design vectors to consider in the stopping criteria.

  By default it is set to 3.

• store_jacobian : <class 'bool'>, optional

  Whether to store the Jacobian matrices in the database.

  This argument is ignored when the use_database option is False. If a gradient-based algorithm is used, this option cannot be set along with kkt options.

  By default it is set to True.

• use_database : <class 'bool'>, optional

  Whether to wrap the functions in the database.

  By default it is set to True.

• use_one_line_progress_bar : <class 'bool'>, optional

  Whether to log the progress bar on a single line.

  By default it is set to False.

• xtol_abs : <class 'float'>, optional

  The absolute tolerance on the design parameters.

  By default it is set to 0.0.

• xtol_rel : <class 'float'>, optional

  The relative tolerance on the design parameters.

  By default it is set to 0.0.

L-BFGS-B

Module: gemseo.algos.opt.scipy_local.scipy_local

from gemseo.settings.opt import L_BFGS_B_Settings

Limited-memory BFGS algorithm implemented in the SciPy library

More details about the algorithm and its settings on https://docs.scipy.org/doc/scipy/reference/optimize.minimize-lbfgsb.html.

Optional settings

• disp : <class 'bool'>, optional

  Whether to print convergence messages.

  By default it is set to False.

• enable_progress_bar : typing.Optional[bool], optional

  Whether to enable the progress bar in the optimization log.

  If None, use the global value of enable_progress_bar (see the configure function to change it globally).

  By default it is set to None.

• eq_tolerance : <class 'float'>, optional

  The tolerance on the equality constraints.

  By default it is set to 1e-06.

• ftol_abs : <class 'float'>, optional

  The absolute tolerance on the objective function.

  By default it is set to 1e-09.

• ftol_rel : <class 'float'>, optional

  The relative tolerance on the objective function.

  By default it is set to 1e-09.

• gtol : <class 'float'>, optional

  The precision goal for the projected gradient value to stop the algorithm.

  By default it is set to 1e-06.

• ineq_tolerance : <class 'float'>, optional

  The tolerance on the inequality constraints.

  By default it is set to 0.0001.

• iprint : <class 'int'>, optional

  The flag to control the frequency of output.

  Default is no output.

  By default it is set to -1.

• kkt_tol_abs : <class 'float'>, optional

  The absolute tolerance on the KKT residual norm.

  If inf this criterion is not activated.

  By default it is set to inf.

• kkt_tol_rel : <class 'float'>, optional

  The relative tolerance on the KKT residual norm.

  If inf this criterion is not activated.

  By default it is set to inf.

• log_problem : <class 'bool'>, optional

  Whether to log the definition and result of the problem.

  By default it is set to True.

• max_iter : <class 'int'>, optional

  The maximum number of iterations.

  By default it is set to 1000.

• max_time : <class 'float'>, optional

  The maximum runtime in seconds, disabled if 0.

  By default it is set to 0.0.

• maxcor : <class 'int'>, optional

  The maximum number of corrections for the limited memory matrix.

  By default it is set to 20.

• maxls : <class 'int'>, optional

  The maximum number of line search steps per iteration.

  By default it is set to 20.

• normalize_design_space : <class 'bool'>, optional

  Whether to normalize the design space variables between 0 and 1.

  By default it is set to True.

• reset_iteration_counters : <class 'bool'>, optional

  Whether to reset the iteration counters before each execution.

  By default it is set to True.

• round_ints : <class 'bool'>, optional

  Whether to round the integer variables.

  By default it is set to True.

• scaling_threshold : typing.Optional[typing.Annotated[float, Ge(ge=0)]], optional

  The threshold on the reference function value that triggers scaling.

  If None, do not scale the functions.

  By default it is set to None.

• stop_crit_n_x : <class 'int'>, optional

  The minimum number of design vectors to consider in the stopping criteria.

  By default it is set to 3.

• store_jacobian : <class 'bool'>, optional

  Whether to store the Jacobian matrices in the database.

  This argument is ignored when the use_database option is False. If a gradient-based algorithm is used, this option cannot be set along with kkt options.

  By default it is set to True.

• use_database : <class 'bool'>, optional

  Whether to wrap the functions in the database.

  By default it is set to True.

• use_one_line_progress_bar : <class 'bool'>, optional

  Whether to log the progress bar on a single line.

  By default it is set to False.

• xtol_abs : <class 'float'>, optional

  The absolute tolerance on the design parameters.

  By default it is set to 1e-09.

• xtol_rel : <class 'float'>, optional

  The relative tolerance on the design parameters.

  By default it is set to 1e-09.

MNBI

Module: gemseo.algos.opt.mnbi.mnbi

from gemseo.settings.opt import MNBI_Settings

Modified Normal Boundary Intersection (mNBI) method

Required settings

• sub_optim_algo : <class 'str'>

  The optimization algorithm used to solve the sub-optimization problems.

Optional settings

• custom_anchor_points : collections.abc.Sequence[gemseo.utils.pydantic_ndarray._NDArrayPydantic[typing.Any, numpy.dtype[+_ScalarType_co]]], optional

  The bounding points of the custom phi simplex for the optimization.

  By default it is set to ().

• custom_phi_betas : collections.abc.Sequence[gemseo.utils.pydantic_ndarray._NDArrayPydantic[typing.Any, numpy.dtype[+_ScalarType_co]]], optional

  The custom values of \(\\Phi \beta\) to be used in the optimization.

  By default it is set to ().

• debug : <class 'bool'>, optional

  Whether to output the sub-optimization optima in a database hdf file.

  By default it is set to False.

• debug_file_path : typing.Union[str, pathlib.Path], optional

  The path to the debug file if debug mode is active.

  By default it is set to debug_history.h5.

• doe_algo : <class 'str'>, optional

  The design of experiments algo for the target points on the Pareto front.

  A fullfactorial DOE is used default as these tend to be low dimensions, usually not more than 3 objectives for a given problem. This setting is relevant only for problems with more than 2 objectives.

  By default it is set to PYDOE_FULLFACT.

• doe_algo_settings : collections.abc.Mapping[str, typing.Any], optional

  The settings for the DOE algorithm.

  By default it is set to {}.

• enable_progress_bar : typing.Optional[bool], optional

  Whether to enable the progress bar in the optimization log.

  If None, use the global value of enable_progress_bar (see the configure function to change it globally).

  By default it is set to None.

• eq_tolerance : <class 'float'>, optional

  The tolerance on the equality constraints.

  By default it is set to 0.01.

• ftol_abs : <class 'float'>, optional

  The absolute tolerance on the objective function.

  By default it is set to 0.0.

• ftol_rel : <class 'float'>, optional

  The relative tolerance on the objective function.

  By default it is set to 0.0.

• ineq_tolerance : <class 'float'>, optional

  The tolerance on the inequality constraints.

  By default it is set to 0.0001.

• log_problem : <class 'bool'>, optional

  Whether to log the definition and result of the problem.

  By default it is set to True.

• max_iter : <class 'int'>, optional

  The maximum number of iterations.

  By default it is set to 1000.

• max_time : <class 'float'>, optional

  The maximum runtime in seconds, disabled if 0.

  By default it is set to 0.0.

• n_processes : <class 'int'>, optional

  The maximum number of processes used to parallelize the sub-optimizations.

  By default it is set to 1.

• n_sub_optim : <class 'int'>, optional

  The number of sub-optimizations points.

  mNBI generates n_sub_optim points on the Pareto front between the n-objective individual minima. This value must be strictly greater than the number of objectives of the problem.

  By default it is set to 1.

• normalize_design_space : <class 'bool'>, optional

  Whether to normalize the design space variables between 0 and 1.

  The mNBI algorithm does not allow to normalize the design space at the top level, only the sub-optimizations accept design space normalization. To do this, pass the setting normalize_design_space to sub_optim_algo_settings.

  By default it is set to False.

• reset_iteration_counters : <class 'bool'>, optional

  Whether to reset the iteration counters before each execution.

  By default it is set to True.

• round_ints : <class 'bool'>, optional

  Whether to round the integer variables.

  By default it is set to True.

• scaling_threshold : typing.Optional[typing.Annotated[float, Ge(ge=0)]], optional

  The threshold on the reference function value that triggers scaling.

  If None, do not scale the functions.

  By default it is set to None.

• skip_betas : <class 'bool'>, optional

  Whether to skip the sub-optimizations of relevant.

  The sub-optimizations are skipped if they correspond to values of beta for which the theoretical result has already been found.

  By default it is set to True.

• stop_crit_n_x : <class 'int'>, optional

  The minimum number of design vectors to consider in the stopping criteria.

  By default it is set to 3.

• store_jacobian : <class 'bool'>, optional

  Whether to store the Jacobian matrices in the database.

  This argument is ignored when the use_database option is False. If a gradient-based algorithm is used, this option cannot be set along with kkt options.

  By default it is set to True.

• sub_optim_algo_settings : collections.abc.Mapping[str, typing.Any], optional

  The settings for the sub optimization algorithm.

  By default it is set to {}.

• sub_optim_max_iter : <class 'int'>, optional

  The maximum number of iterations of the sub-optimization algorithms.

  If 0, the max_iter value is used.

  By default it is set to 0.

• use_database : <class 'bool'>, optional

  Whether to wrap the functions in the database.

  By default it is set to True.

• use_one_line_progress_bar : <class 'bool'>, optional

  Whether to log the progress bar on a single line.

  By default it is set to False.

• xtol_abs : <class 'float'>, optional

  The absolute tolerance on the design parameters.

  By default it is set to 0.0.

• xtol_rel : <class 'float'>, optional

  The relative tolerance on the design parameters.

  By default it is set to 0.0.

MultiStart

Module: gemseo.algos.opt.multi_start.multi_start

from gemseo.settings.opt import MultiStart_Settings

The optimization algorithm multistart generates starting points using a DOE algorithmand run a sub-optimization algorithm from each starting point.Depending on the sub-optimization algorithm,``multistart`` can handle integer design variables,equality and inequality constraintsas well as multi-objective functions.

Optional settings

• doe_algo_name : <class 'str'>, optional

  The name of the DOE algorithm.

  The DOE algorthm is used to generate the sub-optimizations starting points.

  By default it is set to LHS.

• doe_algo_settings : collections.abc.Mapping[str, typing.Any], optional

  The settings of the DOE algorithm.

  By default it is set to {}.

• enable_progress_bar : typing.Optional[bool], optional

  Whether to enable the progress bar in the optimization log.

  If None, use the global value of enable_progress_bar (see the configure function to change it globally).

  By default it is set to None.

• eq_tolerance : <class 'float'>, optional

  The tolerance on the equality constraints.

  By default it is set to 0.01.

• ftol_abs : <class 'float'>, optional

  The absolute tolerance on the objective function.

  By default it is set to 0.0.

• ftol_rel : <class 'float'>, optional

  The relative tolerance on the objective function.

  By default it is set to 0.0.

• ineq_tolerance : <class 'float'>, optional

  The tolerance on the inequality constraints.

  By default it is set to 0.0001.

• log_problem : <class 'bool'>, optional

  Whether to log the definition and result of the problem.

  By default it is set to True.

• max_iter : <class 'int'>, optional

  The maximum number of iterations.

  By default it is set to 1000.

• max_time : <class 'float'>, optional

  The maximum runtime in seconds, disabled if 0.

  By default it is set to 0.0.

• multistart_file_path : typing.Union[str, pathlib.Path]

  The database file path to save the local optima.

  If empty, do not save the local optima.

  By default it is set to .

• n_processes : <class 'int'>, optional

  The maximum number of processes used to parallelize the sub-optimizations.

  By default it is set to 1.

• n_start : <class 'int'>, optional

  The number of sub-optimizations.

  By default it is set to 5.

• normalize_design_space : <class 'bool'>, optional

  Whether to normalize the design space variables between 0 and 1.

  By default it is set to False.

• opt_algo_max_iter : <class 'int'>, optional

  The maximum number of iterations for each sub-optimization.

  If 0, this number is int(max_iter/n_start).

  By default it is set to 0.

• opt_algo_name : <class 'str'>, optional

  The name of the sub-optimization algorithm.

  By default it is set to SLSQP.

• opt_algo_settings : collections.abc.Mapping[str, typing.Any], optional

  The settings of the sub-optimization algorithm.

  By default it is set to {}.

• reset_iteration_counters : <class 'bool'>, optional

  Whether to reset the iteration counters before each execution.

  By default it is set to True.

• round_ints : <class 'bool'>, optional

  Whether to round the integer variables.

  By default it is set to True.

• scaling_threshold : typing.Optional[typing.Annotated[float, Ge(ge=0)]], optional

  The threshold on the reference function value that triggers scaling.

  If None, do not scale the functions.

  By default it is set to None.

• stop_crit_n_x : <class 'int'>, optional

  The minimum number of design vectors to consider in the stopping criteria.

  By default it is set to 3.

• store_jacobian : <class 'bool'>, optional

  Whether to store the Jacobian matrices in the database.

  This argument is ignored when the use_database option is False. If a gradient-based algorithm is used, this option cannot be set along with kkt options.

  By default it is set to True.

• use_database : <class 'bool'>, optional

  Whether to wrap the functions in the database.

  By default it is set to True.

• use_one_line_progress_bar : <class 'bool'>, optional

  Whether to log the progress bar on a single line.

  By default it is set to False.

• xtol_abs : <class 'float'>, optional

  The absolute tolerance on the design parameters.

  By default it is set to 0.0.

• xtol_rel : <class 'float'>, optional

  The relative tolerance on the design parameters.

  By default it is set to 0.0.

NELDER-MEAD

Module: gemseo.algos.opt.scipy_local.scipy_local

from gemseo.settings.opt import NELDER_MEAD_Settings

Nelder-Mead algorithm implemented in the SciPy library

More details about the algorithm and its settings on https://docs.scipy.org/doc/scipy/reference/optimize.minimize-neldermead.html.

Optional settings

• adaptive : <class 'bool'>, optional

  Whether to adapt the algorithm parameters to dimensionality of problem.

  By default it is set to False.

• disp : <class 'bool'>, optional

  Whether to print convergence messages.

  By default it is set to False.

• enable_progress_bar : typing.Optional[bool], optional

  Whether to enable the progress bar in the optimization log.

  If None, use the global value of enable_progress_bar (see the configure function to change it globally).

  By default it is set to None.

• eq_tolerance : <class 'float'>, optional

  The tolerance on the equality constraints.

  By default it is set to 1e-06.

• ftol_abs : <class 'float'>, optional

  The absolute tolerance on the objective function.

  By default it is set to 1e-09.

• ftol_rel : <class 'float'>, optional

  The relative tolerance on the objective function.

  By default it is set to 1e-09.

• ineq_tolerance : <class 'float'>, optional

  The tolerance on the inequality constraints.

  By default it is set to 0.0001.

• initial_simplex : typing.Union[collections.abc.Sequence[float], gemseo.utils.pydantic_ndarray._NDArrayPydantic[typing.Any, numpy.dtype[float]], NoneType], optional

  The initial simplex.

  If provided, the expected shape is (N+1, N) where N is the problem dimension.

  By default it is set to None.

• log_problem : <class 'bool'>, optional

  Whether to log the definition and result of the problem.

  By default it is set to True.

• max_iter : <class 'int'>, optional

  The maximum number of iterations.

  By default it is set to 1000.

• max_time : <class 'float'>, optional

  The maximum runtime in seconds, disabled if 0.

  By default it is set to 0.0.

• normalize_design_space : <class 'bool'>, optional

  Whether to normalize the design space variables between 0 and 1.

  By default it is set to True.

• reset_iteration_counters : <class 'bool'>, optional

  Whether to reset the iteration counters before each execution.

  By default it is set to True.

• return_all : <class 'bool'>, optional

  Whether to return a list of the best solution at each of the iterations.

  By default it is set to False.

• round_ints : <class 'bool'>, optional

  Whether to round the integer variables.

  By default it is set to True.

• scaling_threshold : typing.Optional[typing.Annotated[float, Ge(ge=0)]], optional

  The threshold on the reference function value that triggers scaling.

  If None, do not scale the functions.

  By default it is set to None.

• stop_crit_n_x : <class 'int'>, optional

  The minimum number of design vectors to consider in the stopping criteria.

  By default it is set to 3.

• store_jacobian : <class 'bool'>, optional

  Whether to store the Jacobian matrices in the database.

  This argument is ignored when the use_database option is False. If a gradient-based algorithm is used, this option cannot be set along with kkt options.

  By default it is set to True.

• use_database : <class 'bool'>, optional

  Whether to wrap the functions in the database.

  By default it is set to True.

• use_one_line_progress_bar : <class 'bool'>, optional

  Whether to log the progress bar on a single line.

  By default it is set to False.

• xtol_abs : <class 'float'>, optional

  The absolute tolerance on the design parameters.

  By default it is set to 1e-09.

• xtol_rel : <class 'float'>, optional

  The relative tolerance on the design parameters.

  By default it is set to 1e-09.

NLOPT_BFGS

Module: gemseo.algos.opt.nlopt.nlopt

from gemseo.settings.opt import NLOPT_BFGS_Settings

Broyden-Fletcher-Goldfarb-Shanno method (BFGS) implemented in the NLOPT library

More details about the algorithm and its settings on https://nlopt.readthedocs.io/en/latest/NLopt_Algorithms/#low-storage-bfgs.

Optional settings

• enable_progress_bar : typing.Optional[bool], optional

  Whether to enable the progress bar in the optimization log.

  If None, use the global value of enable_progress_bar (see the configure function to change it globally).

  By default it is set to None.

• eq_tolerance : <class 'float'>, optional

  The tolerance on the equality constraints.

  By default it is set to 0.01.

• ftol_abs : <class 'float'>, optional

  The absolute tolerance on the objective function.

  By default it is set to 1e-14.

• ftol_rel : <class 'float'>, optional

  The relative tolerance on the objective function.

  By default it is set to 1e-08.

• ineq_tolerance : <class 'float'>, optional

  The tolerance on the inequality constraints.

  By default it is set to 0.0001.

• kkt_tol_abs : <class 'float'>, optional

  The absolute tolerance on the KKT residual norm.

  If inf this criterion is not activated.

  By default it is set to inf.

• kkt_tol_rel : <class 'float'>, optional

  The relative tolerance on the KKT residual norm.

  If inf this criterion is not activated.

  By default it is set to inf.

• log_problem : <class 'bool'>, optional

  Whether to log the definition and result of the problem.

  By default it is set to True.

• max_iter : <class 'int'>, optional

  The maximum number of iterations.

  By default it is set to 1000.

• max_time : <class 'float'>, optional

  The maximum runtime in seconds, disabled if 0.

  By default it is set to 0.0.

• normalize_design_space : <class 'bool'>, optional

  Whether to normalize the design space variables between 0 and 1.

  By default it is set to True.

• reset_iteration_counters : <class 'bool'>, optional

  Whether to reset the iteration counters before each execution.

  By default it is set to True.

• round_ints : <class 'bool'>, optional

  Whether to round the integer variables.

  By default it is set to True.

• scaling_threshold : typing.Optional[typing.Annotated[float, Ge(ge=0)]], optional

  The threshold on the reference function value that triggers scaling.

  If None, do not scale the functions.

  By default it is set to None.

• stop_crit_n_x : typing.Optional[int], optional

  The minimum number of design vectors to consider in the stopping criteria.

  By default it is set to None.

• stopval : <class 'float'>, optional

  The objective value at which the optimization will stop.

  By default it is set to -inf.

• store_jacobian : <class 'bool'>, optional

  Whether to store the Jacobian matrices in the database.

  This argument is ignored when the use_database option is False. If a gradient-based algorithm is used, this option cannot be set along with kkt options.

  By default it is set to True.

• use_database : <class 'bool'>, optional

  Whether to wrap the functions in the database.

  By default it is set to True.

• use_one_line_progress_bar : <class 'bool'>, optional

  Whether to log the progress bar on a single line.

  By default it is set to False.

• xtol_abs : <class 'float'>, optional

  The absolute tolerance on the design parameters.

  By default it is set to 1e-14.

• xtol_rel : <class 'float'>, optional

  The relative tolerance on the design parameters.

  By default it is set to 1e-08.

NLOPT_BOBYQA

Module: gemseo.algos.opt.nlopt.nlopt

from gemseo.settings.opt import NLOPT_BOBYQA_Settings

Bound Optimization BY Quadratic Approximation (BOBYQA) implemented in the NLOPT library

More details about the algorithm and its settings on https://nlopt.readthedocs.io/en/latest/NLopt_Algorithms/#bobyqa.

Optional settings

• enable_progress_bar : typing.Optional[bool], optional

  Whether to enable the progress bar in the optimization log.

  If None, use the global value of enable_progress_bar (see the configure function to change it globally).

  By default it is set to None.

• eq_tolerance : <class 'float'>, optional

  The tolerance on the equality constraints.

  By default it is set to 0.01.

• ftol_abs : <class 'float'>, optional

  The absolute tolerance on the objective function.

  By default it is set to 1e-14.

• ftol_rel : <class 'float'>, optional

  The relative tolerance on the objective function.

  By default it is set to 1e-08.

• ineq_tolerance : <class 'float'>, optional

  The tolerance on the inequality constraints.

  By default it is set to 0.0001.

• init_step : typing.Union[typing.Annotated[float, Gt(gt=0)], gemseo.utils.pydantic_ndarray._NDArrayPydantic[typing.Any, numpy.dtype[typing.Annotated[float, Gt(gt=0)]]]], optional

  The initial step size for derivative-free algorithms.

  It can be an array of the initial steps for each dimension, or a single number if the same step will be used for all of them.

  For derivative-free local-optimization algorithms, the optimizer must somehow decide on some initial step size to perturb x by when it begins the optimization. This step size should be big enough so that the value of the objective significantly changes, but not too big if you want to find the local optimum nearest to x.

  By default it is set to 0.25.

• log_problem : <class 'bool'>, optional

  Whether to log the definition and result of the problem.

  By default it is set to True.

• max_iter : <class 'int'>, optional

  The maximum number of iterations.

  By default it is set to 1000.

• max_time : <class 'float'>, optional

  The maximum runtime in seconds, disabled if 0.

  By default it is set to 0.0.

• normalize_design_space : <class 'bool'>, optional

  Whether to normalize the design space variables between 0 and 1.

  By default it is set to True.

• reset_iteration_counters : <class 'bool'>, optional

  Whether to reset the iteration counters before each execution.

  By default it is set to True.

• round_ints : <class 'bool'>, optional

  Whether to round the integer variables.

  By default it is set to True.

• scaling_threshold : typing.Optional[typing.Annotated[float, Ge(ge=0)]], optional

  The threshold on the reference function value that triggers scaling.

  If None, do not scale the functions.

  By default it is set to None.

• stop_crit_n_x : typing.Optional[int], optional

  The minimum number of design vectors to consider in the stopping criteria.

  By default it is set to None.

• stopval : <class 'float'>, optional

  The objective value at which the optimization will stop.

  By default it is set to -inf.

• store_jacobian : <class 'bool'>, optional

  Whether to store the Jacobian matrices in the database.

  This argument is ignored when the use_database option is False. If a gradient-based algorithm is used, this option cannot be set along with kkt options.

  By default it is set to True.

• use_database : <class 'bool'>, optional

  Whether to wrap the functions in the database.

  By default it is set to True.

• use_one_line_progress_bar : <class 'bool'>, optional

  Whether to log the progress bar on a single line.

  By default it is set to False.

• xtol_abs : <class 'float'>, optional

  The absolute tolerance on the design parameters.

  By default it is set to 1e-14.

• xtol_rel : <class 'float'>, optional

  The relative tolerance on the design parameters.

  By default it is set to 1e-08.

NLOPT_COBYLA

Module: gemseo.algos.opt.nlopt.nlopt

from gemseo.settings.opt import NLOPT_COBYLA_Settings

Constrained Optimization BY Linear Approximations (COBYLA) implemented in the NLOPT library

More details about the algorithm and its settings on https://nlopt.readthedocs.io/en/latest/NLopt_Algorithms/#cobyla-constrained-optimization-by-linear-approximations.

Optional settings

• enable_progress_bar : typing.Optional[bool], optional

  Whether to enable the progress bar in the optimization log.

  If None, use the global value of enable_progress_bar (see the configure function to change it globally).

  By default it is set to None.

• eq_tolerance : <class 'float'>, optional

  The tolerance on the equality constraints.

  By default it is set to 0.01.

• ftol_abs : <class 'float'>, optional

  The absolute tolerance on the objective function.

  By default it is set to 1e-14.

• ftol_rel : <class 'float'>, optional

  The relative tolerance on the objective function.

  By default it is set to 1e-08.

• ineq_tolerance : <class 'float'>, optional

  The tolerance on the inequality constraints.

  By default it is set to 0.0001.

• init_step : typing.Union[typing.Annotated[float, Gt(gt=0)], gemseo.utils.pydantic_ndarray._NDArrayPydantic[typing.Any, numpy.dtype[typing.Annotated[float, Gt(gt=0)]]]], optional

  The initial step size for derivative-free algorithms.

  It can be an array of the initial steps for each dimension, or a single number if the same step will be used for all of them.

  For derivative-free local-optimization algorithms, the optimizer must somehow decide on some initial step size to perturb x by when it begins the optimization. This step size should be big enough so that the value of the objective significantly changes, but not too big if you want to find the local optimum nearest to x.

  By default it is set to 0.25.

• log_problem : <class 'bool'>, optional

  Whether to log the definition and result of the problem.

  By default it is set to True.

• max_iter : <class 'int'>, optional

  The maximum number of iterations.

  By default it is set to 1000.

• max_time : <class 'float'>, optional

  The maximum runtime in seconds, disabled if 0.

  By default it is set to 0.0.

• normalize_design_space : <class 'bool'>, optional

  Whether to normalize the design space variables between 0 and 1.

  By default it is set to True.

• reset_iteration_counters : <class 'bool'>, optional

  Whether to reset the iteration counters before each execution.

  By default it is set to True.

• round_ints : <class 'bool'>, optional

  Whether to round the integer variables.

  By default it is set to True.

• scaling_threshold : typing.Optional[typing.Annotated[float, Ge(ge=0)]], optional

  The threshold on the reference function value that triggers scaling.

  If None, do not scale the functions.

  By default it is set to None.

• stop_crit_n_x : typing.Optional[int], optional

  The minimum number of design vectors to consider in the stopping criteria.

  By default it is set to None.

• stopval : <class 'float'>, optional

  The objective value at which the optimization will stop.

  By default it is set to -inf.

• store_jacobian : <class 'bool'>, optional

  Whether to store the Jacobian matrices in the database.

  This argument is ignored when the use_database option is False. If a gradient-based algorithm is used, this option cannot be set along with kkt options.

  By default it is set to True.

• use_database : <class 'bool'>, optional

  Whether to wrap the functions in the database.

  By default it is set to True.

• use_one_line_progress_bar : <class 'bool'>, optional

  Whether to log the progress bar on a single line.

  By default it is set to False.

• xtol_abs : <class 'float'>, optional

  The absolute tolerance on the design parameters.

  By default it is set to 1e-14.

• xtol_rel : <class 'float'>, optional

  The relative tolerance on the design parameters.

  By default it is set to 1e-08.

NLOPT_MMA

Module: gemseo.algos.opt.nlopt.nlopt

from gemseo.settings.opt import NLOPT_MMA_Settings

Method of Moving Asymptotes (MMA)implemented in the NLOPT library

More details about the algorithm and its settings on https://nlopt.readthedocs.io/en/latest/NLopt_Algorithms/#mma-method-of-moving-asymptotes-and-ccsa.

Optional settings

• enable_progress_bar : typing.Optional[bool], optional

  Whether to enable the progress bar in the optimization log.

  If None, use the global value of enable_progress_bar (see the configure function to change it globally).

  By default it is set to None.

• eq_tolerance : <class 'float'>, optional

  The tolerance on the equality constraints.

  By default it is set to 0.01.

• ftol_abs : <class 'float'>, optional

  The absolute tolerance on the objective function.

  By default it is set to 1e-14.

• ftol_rel : <class 'float'>, optional

  The relative tolerance on the objective function.

  By default it is set to 1e-08.

• ineq_tolerance : <class 'float'>, optional

  The tolerance on the inequality constraints.

  By default it is set to 0.0001.

• inner_maxeval : <class 'int'>, optional

  The maximum number of inner iterations of the algorithm.

  The value 0 means that there is no limit.

  By default it is set to 0.

• kkt_tol_abs : <class 'float'>, optional

  The absolute tolerance on the KKT residual norm.

  If inf this criterion is not activated.

  By default it is set to inf.

• kkt_tol_rel : <class 'float'>, optional

  The relative tolerance on the KKT residual norm.

  If inf this criterion is not activated.

  By default it is set to inf.

• log_problem : <class 'bool'>, optional

  Whether to log the definition and result of the problem.

  By default it is set to True.

• max_iter : <class 'int'>, optional

  The maximum number of iterations.

  By default it is set to 1000.

• max_time : <class 'float'>, optional

  The maximum runtime in seconds, disabled if 0.

  By default it is set to 0.0.

• normalize_design_space : <class 'bool'>, optional

  Whether to normalize the design space variables between 0 and 1.

  By default it is set to True.

• reset_iteration_counters : <class 'bool'>, optional

  Whether to reset the iteration counters before each execution.

  By default it is set to True.

• round_ints : <class 'bool'>, optional

  Whether to round the integer variables.

  By default it is set to True.

• scaling_threshold : typing.Optional[typing.Annotated[float, Ge(ge=0)]], optional

  The threshold on the reference function value that triggers scaling.

  If None, do not scale the functions.

  By default it is set to None.

• stop_crit_n_x : typing.Optional[int], optional

  The minimum number of design vectors to consider in the stopping criteria.

  By default it is set to None.

• stopval : <class 'float'>, optional

  The objective value at which the optimization will stop.

  By default it is set to -inf.

• store_jacobian : <class 'bool'>, optional

  Whether to store the Jacobian matrices in the database.

  This argument is ignored when the use_database option is False. If a gradient-based algorithm is used, this option cannot be set along with kkt options.

  By default it is set to True.

• use_database : <class 'bool'>, optional

  Whether to wrap the functions in the database.

  By default it is set to True.

• use_one_line_progress_bar : <class 'bool'>, optional

  Whether to log the progress bar on a single line.

  By default it is set to False.

• xtol_abs : <class 'float'>, optional

  The absolute tolerance on the design parameters.

  By default it is set to 1e-14.

• xtol_rel : <class 'float'>, optional

  The relative tolerance on the design parameters.

  By default it is set to 1e-08.

NLOPT_NEWUOA

Module: gemseo.algos.opt.nlopt.nlopt

from gemseo.settings.opt import NLOPT_NEWUOA_Settings

NEWUOA + bound constraints implemented in the NLOPT library

More details about the algorithm and its settings on https://nlopt.readthedocs.io/en/latest/NLopt_Algorithms/#newuoa-bound-constraints.

Optional settings

• enable_progress_bar : typing.Optional[bool], optional

  Whether to enable the progress bar in the optimization log.

  If None, use the global value of enable_progress_bar (see the configure function to change it globally).

  By default it is set to None.

• eq_tolerance : <class 'float'>, optional

  The tolerance on the equality constraints.

  By default it is set to 0.01.

• ftol_abs : <class 'float'>, optional

  The absolute tolerance on the objective function.

  By default it is set to 1e-14.

• ftol_rel : <class 'float'>, optional

  The relative tolerance on the objective function.

  By default it is set to 1e-08.

• ineq_tolerance : <class 'float'>, optional

  The tolerance on the inequality constraints.

  By default it is set to 0.0001.

• init_step : typing.Union[typing.Annotated[float, Gt(gt=0)], gemseo.utils.pydantic_ndarray._NDArrayPydantic[typing.Any, numpy.dtype[typing.Annotated[float, Gt(gt=0)]]]], optional

  The initial step size for derivative-free algorithms.

  It can be an array of the initial steps for each dimension, or a single number if the same step will be used for all of them.

  For derivative-free local-optimization algorithms, the optimizer must somehow decide on some initial step size to perturb x by when it begins the optimization. This step size should be big enough so that the value of the objective significantly changes, but not too big if you want to find the local optimum nearest to x.

  By default it is set to 0.25.

• log_problem : <class 'bool'>, optional

  Whether to log the definition and result of the problem.

  By default it is set to True.

• max_iter : <class 'int'>, optional

  The maximum number of iterations.

  By default it is set to 1000.

• max_time : <class 'float'>, optional

  The maximum runtime in seconds, disabled if 0.

  By default it is set to 0.0.

• normalize_design_space : <class 'bool'>, optional

  Whether to normalize the design space variables between 0 and 1.

  By default it is set to True.

• reset_iteration_counters : <class 'bool'>, optional

  Whether to reset the iteration counters before each execution.

  By default it is set to True.

• round_ints : <class 'bool'>, optional

  Whether to round the integer variables.

  By default it is set to True.

• scaling_threshold : typing.Optional[typing.Annotated[float, Ge(ge=0)]], optional

  The threshold on the reference function value that triggers scaling.

  If None, do not scale the functions.

  By default it is set to None.

• stop_crit_n_x : typing.Optional[int], optional

  The minimum number of design vectors to consider in the stopping criteria.

  By default it is set to None.

• stopval : <class 'float'>, optional

  The objective value at which the optimization will stop.

  By default it is set to -inf.

• store_jacobian : <class 'bool'>, optional

  Whether to store the Jacobian matrices in the database.

  This argument is ignored when the use_database option is False. If a gradient-based algorithm is used, this option cannot be set along with kkt options.

  By default it is set to True.

• use_database : <class 'bool'>, optional

  Whether to wrap the functions in the database.

  By default it is set to True.

• use_one_line_progress_bar : <class 'bool'>, optional

  Whether to log the progress bar on a single line.

  By default it is set to False.

• xtol_abs : <class 'float'>, optional

  The absolute tolerance on the design parameters.

  By default it is set to 1e-14.

• xtol_rel : <class 'float'>, optional

  The relative tolerance on the design parameters.

  By default it is set to 1e-08.

NLOPT_SLSQP

Module: gemseo.algos.opt.nlopt.nlopt

from gemseo.settings.opt import NLOPT_SLSQP_Settings

Sequential Least-Squares Quadratic Programming (SLSQP) implemented in the NLOPT library

More details about the algorithm and its settings on https://nlopt.readthedocs.io/en/latest/NLopt_Algorithms/#slsqp.

Optional settings

• enable_progress_bar : typing.Optional[bool], optional

  Whether to enable the progress bar in the optimization log.

  If None, use the global value of enable_progress_bar (see the configure function to change it globally).

  By default it is set to None.

• eq_tolerance : <class 'float'>, optional

  The tolerance on the equality constraints.

  By default it is set to 0.01.

• ftol_abs : <class 'float'>, optional

  The absolute tolerance on the objective function.

  By default it is set to 1e-14.

• ftol_rel : <class 'float'>, optional

  The relative tolerance on the objective function.

  By default it is set to 1e-08.

• ineq_tolerance : <class 'float'>, optional

  The tolerance on the inequality constraints.

  By default it is set to 0.0001.

• kkt_tol_abs : <class 'float'>, optional

  The absolute tolerance on the KKT residual norm.

  If inf this criterion is not activated.

  By default it is set to inf.

• kkt_tol_rel : <class 'float'>, optional

  The relative tolerance on the KKT residual norm.

  If inf this criterion is not activated.

  By default it is set to inf.

• log_problem : <class 'bool'>, optional

  Whether to log the definition and result of the problem.

  By default it is set to True.

• max_iter : <class 'int'>, optional

  The maximum number of iterations.

  By default it is set to 1000.

• max_time : <class 'float'>, optional

  The maximum runtime in seconds, disabled if 0.

  By default it is set to 0.0.

• normalize_design_space : <class 'bool'>, optional

  Whether to normalize the design space variables between 0 and 1.

  By default it is set to True.

• reset_iteration_counters : <class 'bool'>, optional

  Whether to reset the iteration counters before each execution.

  By default it is set to True.

• round_ints : <class 'bool'>, optional

  Whether to round the integer variables.

  By default it is set to True.

• scaling_threshold : typing.Optional[typing.Annotated[float, Ge(ge=0)]], optional

  The threshold on the reference function value that triggers scaling.

  If None, do not scale the functions.

  By default it is set to None.

• stop_crit_n_x : typing.Optional[int], optional

  The minimum number of design vectors to consider in the stopping criteria.

  By default it is set to None.

• stopval : <class 'float'>, optional

  The objective value at which the optimization will stop.

  By default it is set to -inf.

• store_jacobian : <class 'bool'>, optional

  Whether to store the Jacobian matrices in the database.

  This argument is ignored when the use_database option is False. If a gradient-based algorithm is used, this option cannot be set along with kkt options.

  By default it is set to True.

• use_database : <class 'bool'>, optional

  Whether to wrap the functions in the database.

  By default it is set to True.

• use_one_line_progress_bar : <class 'bool'>, optional

  Whether to log the progress bar on a single line.

  By default it is set to False.

• xtol_abs : <class 'float'>, optional

  The absolute tolerance on the design parameters.

  By default it is set to 1e-14.

• xtol_rel : <class 'float'>, optional

  The relative tolerance on the design parameters.

  By default it is set to 1e-08.

SHGO

Module: gemseo.algos.opt.scipy_global.scipy_global

from gemseo.settings.opt import SHGO_Settings

Simplicial homology global optimization

More details about the algorithm and its settings on https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.shgo.html.

Optional settings

• enable_progress_bar : typing.Optional[bool], optional

  Whether to enable the progress bar in the optimization log.

  If None, use the global value of enable_progress_bar (see the configure function to change it globally).

  By default it is set to None.

• eq_tolerance : <class 'float'>, optional

  The tolerance on the equality constraints.

  By default it is set to 1e-06.

• ftol_abs : <class 'float'>, optional

  The absolute tolerance on the objective function.

  By default it is set to 1e-09.

• ftol_rel : <class 'float'>, optional

  The relative tolerance on the objective function.

  By default it is set to 1e-09.

• ineq_tolerance : <class 'float'>, optional

  The tolerance on the inequality constraints.

  By default it is set to 0.0001.

• iters : <class 'int'>, optional

  The number of iterations used to construct the simplicial complex.

  By default it is set to 1.

• log_problem : <class 'bool'>, optional

  Whether to log the definition and result of the problem.

  By default it is set to True.

• max_iter : <class 'int'>, optional

  The maximum number of iterations.

  By default it is set to 9223372036854775807.

• max_time : <class 'float'>, optional

  The maximum runtime in seconds, disabled if 0.

  By default it is set to 0.0.

• n : <class 'int'>, optional

  The number of samples used to construct the simplicial complex.

  By default it is set to 100.

• normalize_design_space : <class 'bool'>, optional

  Whether to normalize the design space variables between 0 and 1.

  By default it is set to True.

• options : collections.abc.Mapping[str, typing.Any], optional

  The options for the local optimization algorithm.

  By default it is set to {}.

• reset_iteration_counters : <class 'bool'>, optional

  Whether to reset the iteration counters before each execution.

  By default it is set to True.

• round_ints : <class 'bool'>, optional

  Whether to round the integer variables.

  By default it is set to True.

• sampling_method : <class 'str'>, optional

  The sampling method.

  By default it is set to simplicial.

• scaling_threshold : typing.Optional[typing.Annotated[float, Ge(ge=0)]], optional

  The threshold on the reference function value that triggers scaling.

  If None, do not scale the functions.

  By default it is set to None.

• stop_crit_n_x : <class 'int'>, optional

  The minimum number of design vectors to consider in the stopping criteria.

  By default it is set to 3.

• store_jacobian : <class 'bool'>, optional

  Whether to store the Jacobian matrices in the database.

  This argument is ignored when the use_database option is False. If a gradient-based algorithm is used, this option cannot be set along with kkt options.

  By default it is set to True.

• use_database : <class 'bool'>, optional

  Whether to wrap the functions in the database.

  By default it is set to True.

• use_one_line_progress_bar : <class 'bool'>, optional

  Whether to log the progress bar on a single line.

  By default it is set to False.

• workers : <class 'int'>, optional

  The number workers to parallelize on.

  By default it is set to 1.

• xtol_abs : <class 'float'>, optional

  The absolute tolerance on the design parameters.

  By default it is set to 1e-09.

• xtol_rel : <class 'float'>, optional

  The relative tolerance on the design parameters.

  By default it is set to 1e-09.

SLSQP

Module: gemseo.algos.opt.scipy_local.scipy_local

from gemseo.settings.opt import SLSQP_Settings

Sequential Least-Squares Quadratic Programming (SLSQP) implemented in the SciPy library

More details about the algorithm and its settings on https://docs.scipy.org/doc/scipy/reference/optimize.minimize-slsqp.html.

Optional settings

• disp : <class 'bool'>, optional

  Whether to print convergence messages.

  By default it is set to False.

• enable_progress_bar : typing.Optional[bool], optional

  Whether to enable the progress bar in the optimization log.

  If None, use the global value of enable_progress_bar (see the configure function to change it globally).

  By default it is set to None.

• eq_tolerance : <class 'float'>, optional

  The tolerance on the equality constraints.

  By default it is set to 1e-06.

• ftol_abs : <class 'float'>, optional

  The absolute tolerance on the objective function.

  By default it is set to 1e-09.

• ftol_rel : <class 'float'>, optional

  The relative tolerance on the objective function.

  By default it is set to 1e-09.

• ineq_tolerance : <class 'float'>, optional

  The tolerance on the inequality constraints.

  By default it is set to 0.0001.

• iprint : <class 'int'>, optional

  The flag to control the frequency of output.

  Default is no output.

  By default it is set to -1.

• kkt_tol_abs : <class 'float'>, optional

  The absolute tolerance on the KKT residual norm.

  If inf this criterion is not activated.

  By default it is set to inf.

• kkt_tol_rel : <class 'float'>, optional

  The relative tolerance on the KKT residual norm.

  If inf this criterion is not activated.

  By default it is set to inf.

• log_problem : <class 'bool'>, optional

  Whether to log the definition and result of the problem.

  By default it is set to True.

• max_iter : <class 'int'>, optional

  The maximum number of iterations.

  By default it is set to 1000.

• max_time : <class 'float'>, optional

  The maximum runtime in seconds, disabled if 0.

  By default it is set to 0.0.

• normalize_design_space : <class 'bool'>, optional

  Whether to normalize the design space variables between 0 and 1.

  By default it is set to True.

• reset_iteration_counters : <class 'bool'>, optional

  Whether to reset the iteration counters before each execution.

  By default it is set to True.

• round_ints : <class 'bool'>, optional

  Whether to round the integer variables.

  By default it is set to True.

• scaling_threshold : typing.Optional[typing.Annotated[float, Ge(ge=0)]], optional

  The threshold on the reference function value that triggers scaling.

  If None, do not scale the functions.

  By default it is set to None.

• stop_crit_n_x : <class 'int'>, optional

  The minimum number of design vectors to consider in the stopping criteria.

  By default it is set to 3.

• store_jacobian : <class 'bool'>, optional

  Whether to store the Jacobian matrices in the database.

  This argument is ignored when the use_database option is False. If a gradient-based algorithm is used, this option cannot be set along with kkt options.

  By default it is set to True.

• use_database : <class 'bool'>, optional

  Whether to wrap the functions in the database.

  By default it is set to True.

• use_one_line_progress_bar : <class 'bool'>, optional

  Whether to log the progress bar on a single line.

  By default it is set to False.

• xtol_abs : <class 'float'>, optional

  The absolute tolerance on the design parameters.

  By default it is set to 1e-09.

• xtol_rel : <class 'float'>, optional

  The relative tolerance on the design parameters.

  By default it is set to 1e-09.

Scipy_MILP

Module: gemseo.algos.opt.scipy_milp.scipy_milp

from gemseo.settings.opt import SciPyMILP_Settings

Mixed-integer linear programming

More details about the algorithm and its settings on https://docs.scipy.org/doc/scipy/reference/scipy.optimize.milp.html.

Optional settings

• disp : <class 'bool'>, optional

  Whether to print optimization status during optimization.

  By default it is set to False.

• enable_progress_bar : typing.Optional[bool], optional

  Whether to enable the progress bar in the optimization log.

  If None, use the global value of enable_progress_bar (see the configure function to change it globally).

  By default it is set to None.

• eq_tolerance : <class 'float'>, optional

  The tolerance on the equality constraints.

  By default it is set to 0.01.

• ftol_abs : <class 'float'>, optional

  The absolute tolerance on the objective function.

  By default it is set to 0.0.

• ftol_rel : <class 'float'>, optional

  The relative tolerance on the objective function.

  By default it is set to 0.0.

• ineq_tolerance : <class 'float'>, optional

  The tolerance on the inequality constraints.

  By default it is set to 0.0001.

• log_problem : <class 'bool'>, optional

  Whether to log the definition and result of the problem.

  By default it is set to True.

• max_iter : <class 'int'>, optional

  The maximum number of iterations.

  By default it is set to 1000.

• max_time : <class 'float'>, optional

  The maximum runtime in seconds, disabled if 0.

  By default it is set to 0.0.

• mip_rel_gap : <class 'float'>, optional

  The termination criterion for MIP solver.

  The solver will terminate when the gap between the primal objective value and the dual objective bound, scaled by the primal objective value, is <= mip_rel_gap.

  By default it is set to 0.0.

• node_limit : <class 'int'>, optional

  The maximum number of nodes to solve before stopping.

  By default it is set to 1000.

• normalize_design_space : <class 'bool'>, optional

  Whether to normalize the design space variables between 0 and 1.

  By default it is set to True.

• presolve : <class 'bool'>, optional

  Whether to perform a preliminary analysis on the problem before solving.

  It attempts to detect infeasibility, unboundedness or problem simplifications.

  By default it is set to True.

• reset_iteration_counters : <class 'bool'>, optional

  Whether to reset the iteration counters before each execution.

  By default it is set to True.

• round_ints : <class 'bool'>, optional

  Whether to round the integer variables.

  By default it is set to True.

• scaling_threshold : typing.Optional[typing.Annotated[float, Ge(ge=0)]], optional

  The threshold on the reference function value that triggers scaling.

  If None, do not scale the functions.

  By default it is set to None.

• stop_crit_n_x : <class 'int'>, optional

  The minimum number of design vectors to consider in the stopping criteria.

  By default it is set to 3.

• store_jacobian : <class 'bool'>, optional

  Whether to store the Jacobian matrices in the database.

  This argument is ignored when the use_database option is False. If a gradient-based algorithm is used, this option cannot be set along with kkt options.

  By default it is set to True.

• use_database : <class 'bool'>, optional

  Whether to wrap the functions in the database.

  By default it is set to True.

• use_one_line_progress_bar : <class 'bool'>, optional

  Whether to log the progress bar on a single line.

  By default it is set to False.

• xtol_abs : <class 'float'>, optional

  The absolute tolerance on the design parameters.

  By default it is set to 0.0.

• xtol_rel : <class 'float'>, optional

  The relative tolerance on the design parameters.

  By default it is set to 0.0.

TNC

Module: gemseo.algos.opt.scipy_local.scipy_local

from gemseo.settings.opt import TNC_Settings

Truncated Newton (TNC) algorithm implemented in SciPy library

More details about the algorithm and its settings on https://docs.scipy.org/doc/scipy/reference/optimize.minimize-tnc.html.

Optional settings

• accuracy : <class 'float'>, optional

  The relative precision for finite difference calculations.

  By default it is set to 0.0.

• disp : <class 'bool'>, optional

  Whether to print convergence messages.

  By default it is set to False.

• enable_progress_bar : typing.Optional[bool], optional

  Whether to enable the progress bar in the optimization log.

  If None, use the global value of enable_progress_bar (see the configure function to change it globally).

  By default it is set to None.

• eq_tolerance : <class 'float'>, optional

  The tolerance on the equality constraints.

  By default it is set to 1e-06.

• eta : <class 'float'>, optional

  The severity of the line search.

  By default it is set to -1.

• ftol_abs : <class 'float'>, optional

  The absolute tolerance on the objective function.

  By default it is set to 1e-09.

• ftol_rel : <class 'float'>, optional

  The relative tolerance on the objective function.

  By default it is set to 1e-09.

• gtol : <class 'float'>, optional

  The precision goal for the projected gradient value to stop the algorithm.

  By default it is set to 1e-06.

• ineq_tolerance : <class 'float'>, optional

  The tolerance on the inequality constraints.

  By default it is set to 0.0001.

• kkt_tol_abs : <class 'float'>, optional

  The absolute tolerance on the KKT residual norm.

  If inf this criterion is not activated.

  By default it is set to inf.

• kkt_tol_rel : <class 'float'>, optional

  The relative tolerance on the KKT residual norm.

  If inf this criterion is not activated.

  By default it is set to inf.

• log_problem : <class 'bool'>, optional

  Whether to log the definition and result of the problem.

  By default it is set to True.

• max_iter : <class 'int'>, optional

  The maximum number of iterations.

  By default it is set to 1000.

• max_time : <class 'float'>, optional

  The maximum runtime in seconds, disabled if 0.

  By default it is set to 0.0.

• maxCGit : <class 'int'>, optional

  The maximum number of hessian-vector evaluations per main iteration.

  By default it is set to -1.

• minfev : <class 'float'>, optional

  The minimum function value estimate.

  By default it is set to 0.0.

• normalize_design_space : <class 'bool'>, optional

  Whether to normalize the design space variables between 0 and 1.

  By default it is set to True.

• offset : typing.Optional[float], optional

  The value to subtract from each variable.

  If None, the offsets are (up+low)/2 for interval bounded variables and x for the others.

  By default it is set to None.

• rescale : <class 'float'>, optional

  The log10 scaling factor used to trigger the objectiv function rescaling.

  By default it is set to 1.3.

• reset_iteration_counters : <class 'bool'>, optional

  Whether to reset the iteration counters before each execution.

  By default it is set to True.

• round_ints : <class 'bool'>, optional

  Whether to round the integer variables.

  By default it is set to True.

• scaling_threshold : typing.Optional[typing.Annotated[float, Ge(ge=0)]], optional

  The threshold on the reference function value that triggers scaling.

  If None, do not scale the functions.

  By default it is set to None.

• stepmx : <class 'float'>, optional

  The maximum step for the line search (may be increased during call).

  By default it is set to 0.0.

• stop_crit_n_x : <class 'int'>, optional

  The minimum number of design vectors to consider in the stopping criteria.

  By default it is set to 3.

• store_jacobian : <class 'bool'>, optional

  Whether to store the Jacobian matrices in the database.

  This argument is ignored when the use_database option is False. If a gradient-based algorithm is used, this option cannot be set along with kkt options.

  By default it is set to True.

• use_database : <class 'bool'>, optional

  Whether to wrap the functions in the database.

  By default it is set to True.

• use_one_line_progress_bar : <class 'bool'>, optional

  Whether to log the progress bar on a single line.

  By default it is set to False.

• xtol_abs : <class 'float'>, optional

  The absolute tolerance on the design parameters.

  By default it is set to 1e-09.

• xtol_rel : <class 'float'>, optional

  The relative tolerance on the design parameters.

  By default it is set to 1e-09.