SplitSuperiorization#

class SplitSuperiorization(basic, input_perturbation_scheme=None, target_perturbation_scheme=None)[source]#

Bases: FeasibilityPerturbation

A class used to perform split superiorization on a given feasibility problem.

Parameters:

  • basic (object) – An instance of a split problem.

  • input_perturbation_scheme (Perturbation | None) – Perturbation scheme for the input, by default None.

  • target_perturbation_scheme (Perturbation | None) – Perturbation scheme for the target, by default None.

  • input_objective_tol (float, optional) – Tolerance for the input objective function, by default 1e-4.

  • target_objective_tol (float, optional) – Tolerance for the target objective function, by default 1e-4.

  • prox_tol (float, optional) – Tolerance for the constraint, by default 1e-6.

Attributes:
input_perturbation_schemePerturbation or None

Perturbation scheme for the input.

target_perturbation_schemePerturbation or None

Perturbation scheme for the target.

input_objective_tolfloat

Tolerance for the input objective function.

target_objective_tolfloat

Tolerance for the target objective function.

prox_tolfloat

Tolerance for the constraint.

input_f_kfloat

The current objective function value for the input.

target_f_kfloat

The current objective function value for the target.

p_kfloat

The current proximity function value.

_kint

The current iteration number.

all_x_valueslist

Array storing all points achieved via the superiorization algorithm.

all_function_valueslist

Array storing all objective function values achieved via the superiorization algorithm.

all_x_values_function_reductionlist

Array storing all points achieved via the function reduction step.

all_function_values_function_reductionlist

Array storing all objective function values achieved via the function reduction step.

Methods

solve(x[, max_iter, prox_tol, del_prox_tol, ...])

Solves 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, max_iter=10, prox_tol=1e-06, del_prox_tol=1e-08, del_prox_n=5, proximity_measures=None, del_input_objective_tol=1e-06, del_input_objective_n=5, del_target_objective_tol=1e-06, del_target_objective_n=5, storage=False, storage_iters=None, alternative_stopping_criterion=None, alternative_stopping_criterion_initial_call=None)[source]#

Solves the optimization problem using the superiorization method.

Parameters:

  • x (ndarray[tuple[Any, ...], dtype[TypeVar(_ScalarT, bound= generic)]]) – Starting point for the algorithm.

  • max_iter (int) – Maximum number of iterations to perform, by default 500.

  • prox_tol (float) – The tolerance for the proximity on the constraints, by default 1e-6.

  • del_prox_tol (float) – The tolerance for the change in proximity over the last del_prox_n iterations, by default 1e-8.

  • del_prox_n (int) – The number of iterations that del_prox_tol needs to be met in a row, by default 5.

  • proximity_measures (Optional[List]) – The proximity measures to calculate, by default a l2 norm measure is used. Right now only the first in the list is used to check the feasibility.

  • del_input_objective_tol (float) – The tolerance for change in the objective function over the last del_input_objective_n iterations, by default 1e-8.

  • del_input_objective_n (int) – The number of iterations that del_input_objective_tol needs to be met in a row, by default 5.

  • del_target_objective_tol (float) – The tolerance for change in the objective function over the last del_target_objective_n iterations, by default 1e-8.

  • del_target_objective_n (int) – The number of iterations that del_target_objective_tol needs to be met in a row, by default 5.

  • storage (bool) – Flag indicating whether to store intermediate solutions, by default 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 after performing the superiorization method.

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