Superiorization#

class Superiorization(basic, perturbation_scheme)[source]#

Bases: FeasibilityPerturbation

Superiorization algorithm for constrained optimization problems.

Parameters:

  • basic (Projection) – The underlying feasibility seeking algorithm.

  • perturbation_scheme (Perturbation) – The perturbation scheme to be used for superiorization.

Attributes:
basicCallable

The underlying feasibility seeking algorithm.

perturbation_schemePerturbation

The perturbation scheme to be used for superiorization.

objective_tolfloat

Tolerance for the objective function value change to determine stopping criteria.

prox_tolfloat

Tolerance for the constraint proximity value change to determine stopping criteria.

_kint

The current iteration number.

all_xlist | None

List of all points achieved during the optimization process, only stored if requested by the user.

all_function_valueslist | None

List of all objective function values achieved during the optimization process, only stored if requested by the user.

all_x_function_reductionlist | None

List of all points achieved via the function reduction step, only stored if requested by the user.

all_function_values_function_reductionlist | None

List of all objective function values achieved via the function reduction step, only stored if requested by the user.

all_x_basiclist | None

List of all points achieved via the basic feasibility seeking algorithm, only stored if requested by the user.

all_function_values_basiclist | None

List of all objective function values achieved via the basic feasibility seeking algorithm, only stored if requested by the user.

Methods

solve(x_0[, max_iter, prox_tol, ...])

Solve the optimization problem using the superiorization method.

storage(x, kind[, storage, f, p])

Stores the given values of x and f into the corresponding lists.
solve(x_0, max_iter=10, prox_tol=1e-06, del_prox_tol=1e-08, del_prox_n=5, del_objective_tol=1e-06, del_objective_n=5, proximity_measures=None, storage=False, storage_iters=None, alternative_stopping_criterion=None, alternative_stopping_criterion_initial_call=None)[source]#

Solve the optimization problem using the superiorization method.

Parameters:

  • x_0 (ndarray[tuple[Any, ...], dtype[TypeVar(_ScalarT, bound= generic)]]) – Initial guess for the solution.

  • max_iter (int) – Maximum number of iterations to perform (default is 10).

  • prox_tol (float) – Tolerance for the constraint function value to determine stopping criteria, by default 1e-6.

  • del_prox_tol (float) – Tolerance for the proximity function value change to determine stopping criteria, by default 1e-8.

  • del_prox_n (int) – Number of iterations with proximity changes below the threshold to determine stopping criteria, by default 5.

  • proximity_measures (Optional[List]) – The proximity measures to calculate, by default None. Right now only the first in the list is used to check the feasibility.

  • del_objective_tol (float) – Tolernace for the objective function value to determine stopping criteria, by default 1e-6.

  • del_objective_n (int) – Number of iterations with objective function changes below the threshold to determine stopping criteria, by default 5.

  • storage (bool) – If True, store intermediate results (default is False).

  • storage_iters (Union[List[int], int, None]) – Controls which iterations are stored (when storage=True). If None, all iterations are stored. If a list of ints, only those iteration indices are stored (0 = initial point). If an int, storage occurs every that many iterations.

  • alternative_stopping_criterion (Optional[Callable]) – Alternative stopping criterion

  • alternative_stopping_criterion_initial_call (Optional[Callable]) – Initial call for an alternative stopping criterion

Return type:

ndarray

Returns:

The superiorized solution.

storage(x, kind, storage=True, f=None, p=None)[source]#

Stores the given values of x and f into the corresponding lists.

Parameters:

  • x (ndarray[tuple[Any, ...], dtype[TypeVar(_ScalarT, bound= generic)]]) – The current value of the variable x to be stored.

  • kind (str) – The type of storage to be used, either “function_reduction” or “basic”.

  • storage (bool) – If True, store the values of x