A finitely convergent circumcenter method for the Convex Feasibility Problem
Optimization and Control
2024-10-10 v3
Abstract
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.
Cite
@article{arxiv.2308.09849,
title = {A finitely convergent circumcenter method for the Convex Feasibility Problem},
author = {Roger Behling and Yunier Bello-Cruz and Alfredo Iusem and Di Liu and Luiz-Rafael Santos},
journal= {arXiv preprint arXiv:2308.09849},
year = {2024}
}