English

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.

Keywords

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}
}
R2 v1 2026-06-23T09:06:11.925Z