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

## TL;DR

This paper introduces new finitely convergent deterministic and stochastic iterative methods for solving convex feasibility problems, ensuring convergence under broad control strategies, including cyclic, random, and remote controls.

## Contribution

It presents novel finitely convergent algorithms for convex feasibility problems that work with a wide range of control sequences, including deterministic and stochastic approaches.

## Key findings

- Methods guarantee finite convergence under broad control schemes.
- Applicable to infinite constraint sets with nonempty interior.
- Convergence holds for deterministic and almost surely for stochastic controls.

## 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.