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
nghuychieu@gmail.com
Gue Myung Lee
Dept. of Applied Mathematics, Pukyong National University, Busan 608-737, Republic of Korea
gmlee@pknu.ac.kr
Boris S. Mordukhovich
Dept. of Mathematics, Wayne State University, Detroit, MI 48202, U.S.A.
boris@math.wayne.edu
Tran T. A. Nghia
Dept. of Mathematics and Statistics, Oakland University, Rochester, MI 48309, U.S.A.
nttran@oakland.edu
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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