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Higher‐Order Weakly Generalized Epiderivatives and Applications to Optimality Conditions

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Listed:
  • Qilin Wang
  • Guolin Yu

Abstract

The notions of higher‐order weakly generalized contingent epiderivative and higher‐order weakly generalized adjacent epiderivative for set‐valued maps are proposed. By virtue of the higher‐order weakly generalized contingent (adjacent) epiderivatives, both necessary and sufficient optimality conditions are obtained for Henig efficient solutions to a set‐valued optimization problem whose constraint set is determined by a set‐valued map. The imposed assumptions are relaxed in comparison with those of recent results in the literature. Examples are provided to show some advantages of our notions and results.

Suggested Citation

  • Qilin Wang & Guolin Yu, 2012. "Higher‐Order Weakly Generalized Epiderivatives and Applications to Optimality Conditions," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    • Handle: RePEc:wly:jnljam:v:2012:y:2012:i:1:n:691018
    DOI: 10.1155/2012/691018
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    References listed on IDEAS

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    1. Guang Ya Chen & Johannes Jahn, 1998. "Optimality conditions for set-valued optimization problems," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 48(2), pages 187-200, November.
    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.
    3. Bienvenido Jiménez & Vicente Novo, 2003. "Second order necessary conditions in set constrained differentiable vector optimization," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 58(2), pages 299-317, November.
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