Convergence analysis of variants of the averaged alternating modified reflections method

TL;DR

This paper introduces new variants of the AAMR method for best approximation problems, demonstrating their convergence, convergence rate, and finite termination under certain conditions.

Contribution

The paper develops and analyzes new variants of the AAMR method, providing convergence guarantees and finite termination results.

Findings

Weak convergence established under mild constraints

Convergence rate of the proposed variants shown

Finite termination property proven under interior-point-like condition

Abstract

This paper presents new variants of the averaged alternating modified reflections (AAMR) method for the best approximation problem. Under a mild constraint qualification, we first show its weak convergence and then establish a convergence rate. Furthermore, under a standard interior-point-like condition, we show that the method has a finite termination property.