Variable Metric Quasi-Fej\'er Monotonicity

TL;DR

This paper extends the concept of quasi-Fejér monotonicity to variable metric algorithms, enabling unified convergence analysis for a broader class of optimization and inverse problem algorithms.

Contribution

It introduces a variable metric version of quasi-Fejér monotonicity, broadening its applicability in analyzing convergence of iterative algorithms.

Findings

Extended quasi-Fejér monotonicity to variable metric settings.

Applied the new framework to convex optimization problems.

Demonstrated effectiveness in inverse problems.

Abstract

The notion of quasi-Fej\'er monotonicity has proven to be an efficient tool to simplify and unify the convergence analysis of various algorithms arising in applied nonlinear analysis. In this paper, we extend this notion in the context of variable metric algorithms, whereby the underlying norm is allowed to vary at each iteration. Applications to convex optimization and inverse problems are demonstrated.