Recent progress on Monotone Operator Theory

2012/10/12 by Jonathan M. Borwein, Borwein, Jonathan M., Liangjin Yao +1
Computer Science · Mathematics · #47A06 #47B65 #47H05 (Primary) 46B10 #47N10 #90C25 (Secondary) #Advanced Banach Space Theory #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Optimization and Control (math.OC) #Optimization and Variational Analysis

paper · pdf · doi:10.48550/arxiv.1210.3401

openalex publication_date 2012/10/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we survey recent progress on the theory of maximally monotone operators in general Banach space. We also extend various of the results and leave some open questions.

Related

• Lectures on maximal monotone operators
• Sum of two maximal monotone operators in a general Banach space is maximal
• Maximal monotone operators with non-empty domain interior; characterizations and continuity properties
• Structure theory for maximally monotone operators with points of continuity
• On the surjectivity properties of perturbations of maximal monotone operators in non-reflexive Banach spaces