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Optimality conditions of the set-valued optimization problem with generalized cone convex set-valued maps characterized by contingent epiderivative

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Abstract

In this paper, firstly, a new notion of generalized cone convex set-valued map is introduced in real normed spaces. Secondly, a property of the generalized cone convex set-valued map involving the contingent epiderivative is obtained. Finally, as the applications of this property, we use the contingent epiderivative to establish optimality conditions of the set-valued optimization problem with generalized cone convex set-valued maps in the sense of Henig proper efficiency. The results obtained in this paper generalize and improve some known results in the literature.

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Acknowledgements

The authors are very grateful to reviewers for their valuable advice.

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Authors and Affiliations

  1. College of Sciences, Chongqing University of Technology, Chongqing, 400054, China

    Zhi-ang Zhou

  2. College of Mathematical Sciences, Chongqing Normal University, Chongqing, 400047, China

    Xin-min Yang

  3. Department of Mathematics, Zhejiang Normal University, Jinhua, 321004, China

    Qiu-sheng Qiu

Authors
  1. Zhi-ang Zhou
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  2. Xin-min Yang
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  3. Qiu-sheng Qiu
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Corresponding author

Correspondence to Xin-min Yang.

Additional information

This work was supported by the National Nature Science Foundation of China (11431004,11471291), the General Project of Chongqing Frontier and Applied Foundation Research (cstc2015jcyjA00050) and the Key Project of Chongqing Frontier and Applied Foundation Research (cstc2017jcyjBX0055, cstc2015jcyjBX0113).

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Zhou, Za., Yang, Xm. & Qiu, Qs. Optimality conditions of the set-valued optimization problem with generalized cone convex set-valued maps characterized by contingent epiderivative. Acta Math. Appl. Sin. Engl. Ser. 34, 11–18 (2018). https://doi.org/10.1007/s10255-018-0727-0

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  • DOI: https://doi.org/10.1007/s10255-018-0727-0

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