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Prederivatives of convex set-valued maps and applications to set optimization problems

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  • Michaël Gaydu
  • Michel Geoffroy
  • Yvesner Marcelin

Abstract

We investigate the existence of several kinds of prederivatives for set-valued mappings enjoying convex properties. Then, we established both necessary and sufficient optimality conditions, involving such prederivatives, for set optimization problems. Copyright Springer Science+Business Media New York 2016

Suggested Citation

  • Michaël Gaydu & Michel Geoffroy & Yvesner Marcelin, 2016. "Prederivatives of convex set-valued maps and applications to set optimization problems," Journal of Global Optimization, Springer, vol. 64(1), pages 141-158, January.
    • Handle: RePEc:spr:jglopt:v:64:y:2016:i:1:p:141-158
    DOI: 10.1007/s10898-015-0338-8
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    References listed on IDEAS

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    1. Jean-Pierre Aubin, 1984. "Lipschitz Behavior of Solutions to Convex Minimization Problems," Mathematics of Operations Research, INFORMS, vol. 9(1), pages 87-111, February.
    2. Johannes Jahn & Rüdiger Rauh, 1997. "Contingent epiderivatives and set-valued optimization," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 46(2), pages 193-211, June.
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    Cited by:

    1. Michaël Gaydu & Gilson N. Silva, 2020. "A General Iterative Procedure to Solve Generalized Equations with Differentiable Multifunction," Journal of Optimization Theory and Applications, Springer, vol. 185(1), pages 207-222, April.

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