Coderivative Characterizations of Maximal Monotonicity for Set-Valued Mappings
Nguyễn Huy Chiêu, G. M. Lee, Boris S. Mordukhovich, T. T. A. Nghia · Journal of convex analysis · 2016
This paper concerns generalized differential characterizations of maximal monotone set-valued mappings. Using advanced tools of variational analysis, we establish coderivative criteria for maximal monotonicity of set-valued mappings, which seem to be the first infinitesimal characterizations of maximal monotonicity outside the single-valued case. We also present second-order necessary and sufficient conditions for lower- \mathcal{C}^2 C 2 functions to be convex and strongly convex. Examples are provided to illustrate the obtained results and the imposed assumptions.