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Contingent epiderivatives and set-valued optimization

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  • Johannes Jahn
  • Rüdiger Rauh

Abstract

In this paper we introduce the concept of the contingent epiderivative for a set-valued map which modifies a notion introduced by Aubin [2] as upper contingent derivative. It is shown that this kind of a derivative has important properties and is one possible generalization of directional derivatives in the single-valued convex case. For optimization problems with a set-valued objective function optimality conditions based on the concept of the contingent epiderivative are proved which are necessary and sufficient under suitable assumptions. Copyright Physica-Verlag 1997

Suggested Citation

  • 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.
    • Handle: RePEc:spr:mathme:v:46:y:1997:i:2:p:193-211
    DOI: 10.1007/BF01217690
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