Local Maximal Monotonicity in Variational Analysis and Optimization

TL;DR

This paper systematically studies local maximal monotonicity in variational analysis, providing new characterizations, resolvent conditions, and preservation criteria under summation, with applications to optimization.

Contribution

It introduces novel resolvent characterizations and preservation conditions for local maximal monotonicity in broad infinite-dimensional settings.

Findings

New resolvent characterizations of local maximal monotonicity

Efficient conditions for preservation under summation

Characterizations using generalized differentiation in Hilbert spaces

Abstract

The paper is devoted to a systematic study and characterizations of notions of local maximal monotonicity and their strong counterparts for set-valued operators that appear in variational analysis, optimization, and their applications. We obtain novel resolvent characterizations of these notions together with efficient conditions for their preservation under summation in broad infinite-dimensional settings. Further characterizations of these notions are derived by using generalized differentiation of variational analysis in the framework of Hilbert spaces.