Local Maximal Monotonicity in Variational Analysis and Optimization
系统研究变分分析和优化中集值算子的局部极大单调性及其强形式概念，给出预解式刻画和求和保持条件，并在希尔伯特空间中利用广义微分进一步刻画。
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].