On The Behavior of Subgradient Projections Methods for Convex Feasibility Problems in Euclidean Spaces

TL;DR

This paper investigates subgradient projection methods for convex feasibility problems in Euclidean spaces, introducing a self-adapting relaxation parameter strategy that improves performance in inconsistent cases, supported by numerical experiments.

Contribution

It proposes a novel self-adapting relaxation parameter strategy for subgradient projection methods, enhancing their robustness and efficiency in inconsistent convex feasibility problems.

Findings

The new method demonstrates computational advantages over existing approaches.

The self-adapting strategy guarantees algorithm behavior in inconsistent scenarios.

Numerical experiments validate the improved performance of the proposed method.

Abstract

We study some methods of subgradient projections for solving a convex feasibility problem with general (not necessarily hyperplanes or half-spaces) convex sets in the inconsistent case and propose a strategy that controls the relaxation parameters in a specific self-adapting manner. This strategy leaves enough user-flexibility but gives a mathematical guarantee for the algorithm's behavior in the inconsistent case. We present numerical results of computational experiments that illustrate the computational advantage of the new method.