A note on alternating minimization algorithms: Bregman frame

TL;DR

This paper introduces a unified Bregman frame for classical alternating minimization algorithms, providing a common mathematical formulation and convergence analysis, including stronger results under the Kurdyka-Lojasiewicz property.

Contribution

It proposes a Bregman frame that unifies various alternating minimization algorithms and offers convergence analysis, including under the Kurdyka-Lojasiewicz property.

Findings

Unified mathematical formulation for classical algorithms

Convergence analysis of the Bregman frame

Stronger convergence results under Kurdyka-Lojasiewicz property

Abstract

In this paper, we propose a Bregman frame for several classical alternating minimization algorithms. In the frame, these algorithms have uniform mathematical formulation. We also present convergence analysis for the frame algorithm. Under the Kurdyka-Lojasiewicz property, stronger convergence is obtained.