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-C2\mathcal{C}^2 functions to be convex and strongly convex. Examples are provided to illustrate the obtained results and the imposed assumptions.

Author information

Contact details are reproduced from the original publication and may be historical.

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

Keywords

  • Maximal monotone mappings
  • convex lower-C2 functions
  • variational analysis
  • coderivatives
  • second-order subdifferentials

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Suggested citation

N. H. Chieu, G. M. Lee, B. S. Mordukhovich, T. T. A. Nghia. “Coderivative Characterizations of Maximal Monotonicity for Set-Valued Mappings.” Journal of Convex Analysis 23 (2016), No. 2, 461–480. https://doi.org/10.68381/jca23017

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Published by Heldermann Verlag, 2016. Rights now held by Banach Press.