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New Generalized Second-Order Contingent Epiderivatives and Set-Valued Optimization Problems

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Abstract

In this paper, we introduce the concept of a generalized second-order composed contingent epiderivative for set-valued maps and discuss its relationship to the generalized second-order contingent epiderivative. We also investigate some of its properties. Then, by virtue of the generalized second-order composed contingent epiderivative, we establish a unified second-order sufficient and necessary optimality condition for set-valued optimization problems, which is a generalization of the corresponding results in the literature.

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Authors and Affiliations

  1. College of Mathematics and Statistics, Chongqing University, Chongqing, 401331, China

    S. J. Li & S. K. Zhu

  2. Department of Mathematics and Statistics, Curtin University of Technology, G.P.O. Box U1987, Perth, WA, 6845, Australia

    K. L. Teo

Authors
  1. S. J. Li
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  2. S. K. Zhu
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  3. K. L. Teo
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Correspondence to S. J. Li.

Additional information

Communicated by Guang-ya Chen.

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Li, S.J., Zhu, S.K. & Teo, K.L. New Generalized Second-Order Contingent Epiderivatives and Set-Valued Optimization Problems. J Optim Theory Appl 152, 587–604 (2012). https://doi.org/10.1007/s10957-011-9915-2

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  • DOI: https://doi.org/10.1007/s10957-011-9915-2

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