A finitely convergent circumcenter method for the Convex Feasibility Problem

Fuente: arXiv
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Main Authors: Behling, Roger, Bello-Cruz, Yunier, Iusem, Alfredo, Liu, Di, Santos, Luiz-Rafael
Format: Preprint
Published: 2023
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_version_ 1866916426358456320
author Behling, Roger
Bello-Cruz, Yunier
Iusem, Alfredo
Liu, Di
Santos, Luiz-Rafael
author_facet Behling, Roger
Bello-Cruz, Yunier
Iusem, Alfredo
Liu, Di
Santos, Luiz-Rafael
contents In this paper, we present a variant of the circumcenter method for the Convex Feasibility Problem (CFP), ensuring finite convergence under a Slater assumption. The method replaces exact projections onto the convex sets with projections onto separating halfspaces, perturbed by positive exogenous parameters that decrease to zero along the iterations. If the perturbation parameters decrease slowly enough, such as the terms of a diverging series, finite convergence is achieved. To the best of our knowledge, this is the first circumcenter method for CFP that guarantees finite convergence.
format Preprint
id arxiv_https___arxiv_org_abs_2308_09849
institution arXiv
publishDate 2023
record_format arxiv
spellingShingle A finitely convergent circumcenter method for the Convex Feasibility Problem
Behling, Roger
Bello-Cruz, Yunier
Iusem, Alfredo
Liu, Di
Santos, Luiz-Rafael
Optimization and Control
49M27, 65K05, 65B99, 90C25
In this paper, we present a variant of the circumcenter method for the Convex Feasibility Problem (CFP), ensuring finite convergence under a Slater assumption. The method replaces exact projections onto the convex sets with projections onto separating halfspaces, perturbed by positive exogenous parameters that decrease to zero along the iterations. If the perturbation parameters decrease slowly enough, such as the terms of a diverging series, finite convergence is achieved. To the best of our knowledge, this is the first circumcenter method for CFP that guarantees finite convergence.
title A finitely convergent circumcenter method for the Convex Feasibility Problem
topic Optimization and Control
49M27, 65K05, 65B99, 90C25
url https://arxiv.org/abs/2308.09849