Variable Quasi-Bregman Monotone Sequences

TL;DR

This paper introduces variable quasi-Bregman monotone sequences, unifying existing concepts, and applies this framework to analyze the asymptotic behavior of proximal algorithms and convex feasibility problems in Banach spaces.

Contribution

It proposes a new unified notion of variable quasi-Bregman monotonicity and applies it to analyze convergence of proximal and feasibility algorithms.

Findings

Unified framework for variable quasi-Bregman monotone sequences

Analyzed asymptotic behavior of proximal iterations

Applied results to convex feasibility problems

Abstract

We introduce a notion of variable quasi-Bregman monotone sequence which unifies the notion of variable metric quasi-Fej\'er monotone sequences and that of Bregman monotone sequences. The results are applied to analyze the asymptotic behavior of proximal iterations based on variable Bregman distance and of algorithms for solving convex feasibility problems in reflexive real Banach spaces.