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arXiv · 1905.05660

Finitely Convergent Deterministic and Stochastic Iterative Methods for Solving Convex Feasibility Problems

Victor I. Kolobov·Simeon Reich·Rafał Zalas
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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.

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Victor I. Kolobov, Simeon Reich, Rafał Zalas. 2019-05-14. Finitely Convergent Deterministic and Stochastic Iterative Methods for Solving Convex Feasibility Problems. https://arxiv.org/abs/1905.05660

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