A successive centralized circumcenter reflection method for the convex feasibility problem

TL;DR

This paper introduces a new iterative method for solving convex feasibility problems that converges linearly or superlinearly under certain conditions, with demonstrated numerical efficiency.

Contribution

It develops a successive centralized circumcenter reflection method with convergence guarantees and improved performance under specific assumptions.

Findings

Method converges linearly with most violated constraint control.

Superlinear convergence achieved under smoothness assumptions.

Numerical experiments confirm the method's efficiency.

Abstract

In this paper we present the successive centralization of the circumcenter reflection scheme with several control sequences for solving the convex feasibility problem in Euclidean space. Assuming that a standard error bound holds, we prove the linear convergence of the method with the most violated constraint control sequence. Under additional smoothness assumptions, we prove the superlinear convergence. Numerical experiments confirm the efficiency of our method.