Finitely Convergent Deterministic and Stochastic Iterative Methods for Solving Convex Feasibility Problems
Optimization and Control
2020-09-22 v2
Abstract
We propose finitely convergent methods for solving convex feasibility problems defined over a possibly infinite pool of constraints. Following other works in this area, we assume that the interior of the solution set is nonempty and that certain overrelaxation parameters form a divergent series. We combine our methods with a very general class of deterministic control sequences where, roughly speaking, we require that sooner or later we encounter a violated constraint if one exists. This requirement is satisfied, in particular, by the cyclic, repetitive and remotest set controls. Moreover, it is almost surely satisfied for random controls.
Cite
@article{arxiv.1905.05660,
title = {Finitely Convergent Deterministic and Stochastic Iterative Methods for Solving Convex Feasibility Problems},
author = {Victor I. Kolobov and Simeon Reich and Rafał Zalas},
journal= {arXiv preprint arXiv:1905.05660},
year = {2020}
}