Intriguing maximally monotone operators derived from nonsunny nonexpansive retractions

TL;DR

This paper introduces a novel maximally monotone operator derived from a nonexpansive retraction, expanding the class of known operators beyond traditional subdifferential or linear relation-based examples.

Contribution

It constructs and analyzes a new class of maximally monotone operators not based on subdifferentials or linear relations, focusing on duality and strong monotonicity.

Findings

The operator is maximally monotone and not assembled from traditional components.

Duality properties of the operator are thoroughly analyzed.

Strong monotonicity of the operator is established.

Abstract

Monotone operator theory and fixed point theory for nonexpansive mappings are central areas in modern nonlinear analysis and optimization. Although these areas are fairly well developed, almost all examples published are based on subdifferential operators, linear relations, or combinations thereof. In this paper, we construct an intriguing maximally monotone operator induced by a certain nonexpansive retraction. We analyze this operator, which does not appear to be assembled from subdifferential operators or linear relations, in some detail. Particular emphasis is placed on duality and strong monotonicity.