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Second‐Order Optimality Conditions for Set‐Valued Optimization Problems Under Benson Proper Efficiency

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  • Qilin Wang
  • Guolin Yu

Abstract

Some new properties are obtained for generalized second‐order contingent (adjacent) epiderivatives of set‐valued maps. By employing the generalized second‐order adjacent epiderivatives, necessary and sufficient conditions of Benson proper efficient solutions are given for set‐valued optimization problems. The results obtained improve the corresponding results in the literature.

Suggested Citation

  • Qilin Wang & Guolin Yu, 2011. "Second‐Order Optimality Conditions for Set‐Valued Optimization Problems Under Benson Proper Efficiency," Abstract and Applied Analysis, John Wiley & Sons, vol. 2011(1).
    • Handle: RePEc:wly:jnlaaa:v:2011:y:2011:i:1:n:432963
    DOI: 10.1155/2011/432963
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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. G. Y. Chen & W. D. Rong, 1998. "Characterizations of the Benson Proper Efficiency for Nonconvex Vector Optimization," Journal of Optimization Theory and Applications, Springer, vol. 98(2), pages 365-384, August.
    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.
    4. 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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