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Journal of Convex Analysis 23 (2016), No. 2, 461--480
Copyright Heldermann Verlag 2016

Coderivative Characterizations of Maximal Monotonicity for Set-Valued Mappings

Nguyen Huy Chieu
Dept. of Mathematics, Vinh University, Vinh / Nghe An, Vietnam

Gue Myung Lee
Dept. of Applied Mathematics, Pukyong National University, Busan 608-737, Republic of Korea

Boris S. Mordukhovich
Dept. of Mathematics, Wayne State University, Detroit, MI 48202, U.S.A.

Tran T. A. Nghia
Dept. of Mathematics and Statistics, Oakland University, Rochester, MI 48309, U.S.A.

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-C2 functions to be convex and strongly convex. Examples are provided to illustrate the obtained results and the imposed assumptions.

Keywords: Maximal monotone mappings, convex lower-C2 functions, variational analysis, coderivatives, second-order subdifferentials.

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