Local Maximal Monotonicity in Variational Analysis and Optimization

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. Funding: This research was supported by the U.S. National Science Foundation [Grants DMS-1808978 and DMS-2204519], the Australian Research Council Discovery Project [Grant DP-190100555], and Project 111 of China [Grant D21024].