Rockafellar’s celebrated theorem based on A -maximal monotonicity design

Abstract

A generalization to Rockafellar’s theorem (1976) in the context of approximating a solution to a general inclusion problem involving a set-valued A -maximal monotone mapping using the proximal point algorithm in a Hilbert space setting is presented. Although there exists a vast literature on this theorem, most of the studies are focused on just relaxing the proximal point algorithm and applying to the inclusion problems. The general framework for A -maximal monotonicity (also referred to as the A -monotonicity framework in literature) generalizes the general theory of set-valued maximal monotone mappings, including the H -maximal monotonicity (also referred to as H -monotonicity).