Coderivative characterizations of maximal monotonicity for set-valued mappings

Abstract

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-${\mathcal{C}}^2$ functions to be convex and strongly convex. Examples are provided to illustrate the obtained results and the imposed assumptions.

References in corpus (2)

• Second-order growth, tilt stability, and metric regularity of the subdifferential
• Local strong maximal monotonicity and full stability for parametric variational systems