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Optimality conditions for set-valued optimization problems

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Abstract.

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.

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Authors and Affiliations

  1. Institute of Systems Science, Academia Sinica, Beijing 100080, China, , , , , , CN

    Guang Ya Chen

  2. Institute of Applied Mathematics, University of Erlangen-Nürnberg, Martensstr. 3, D-91058 Erlangen, Germany (e-mail: jahn@am.uni-erlangen.de), , , , , , DE

    Johannes Jahn

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  1. Guang Ya Chen
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  2. Johannes Jahn
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Received April 1997/Revised version March 1998

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Chen, G., Jahn, J. Optimality conditions for set-valued optimization problems. Mathematical Methods of OR 48, 187–200 (1998). https://doi.org/10.1007/s001860050021

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  • DOI: https://doi.org/10.1007/s001860050021

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