Mathematical Methods of Operations Research

, Volume 48, Issue 2, pp 187–200 | Cite as

Optimality conditions for set-valued optimization problems

  • Guang Ya Chen
  • Johannes Jahn


The generalized contingent epiderivative of set-valued maps is introduced in this paper and its relationship to the contingent epiderivative is investigated. A unified necessary and sufficient optimality condition is derived in terms of the generalized contingent epiderivative. The existence of weak subgradients of set-valued maps is proved, and a sufficient optimality condition of set-valued optimization problems is obtained in terms of weak subgradients.

Key words: Set-valued optimization generalized contingent epiderivative optimality conditions subgradient 


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Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Guang Ya Chen
    • 1
  • Johannes Jahn
    • 2
  1. 1.Institute of Systems Science, Academia Sinica, Beijing 100080, ChinaCN
  2. 2.Institute of Applied Mathematics, University of Erlangen-Nürnberg, Martensstr. 3, D-91058 Erlangen, Germany (e-mail:

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