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A Kind of New Higher-Order Mond-Weir Type Duality for Set-Valued Optimization Problems

Author

Listed:
  • Liu He

    (College of Mathematics and Statistics, Chongqing Jiaotong University, Chongqing 400074, China
    Current address: No.66 Xuefu Rd., Nan’an Dist., Chongqing 400074, China.)

  • Qi-Lin Wang

    (College of Mathematics and Statistics, Chongqing Jiaotong University, Chongqing 400074, China)

  • Ching-Feng Wen

    (Center for Fundamental Science; and Research Center for Nonlinear Analysis and Optimization, Kaohsiung Medical University, Kaohsiung 80708, Taiwan
    Department of Medical Research, Kaohsiung Medical University Hospital, Kaohsiung 80708, Taiwan)

  • Xiao-Yan Zhang

    (College of Mathematics and Statistics, Chongqing Jiaotong University, Chongqing 400074, China)

  • Xiao-Bing Li

    (College of Mathematics and Statistics, Chongqing Jiaotong University, Chongqing 400074, China)

Abstract

In this paper, we introduce the notion of higher-order weak adjacent epiderivative for a set-valued map without lower-order approximating directions and obtain existence theorem and some properties of the epiderivative. Then by virtue of the epiderivative and Benson proper efficiency, we establish the higher-order Mond-Weir type dual problem for a set-valued optimization problem and obtain the corresponding weak duality, strong duality and converse duality theorems, respectively.

Suggested Citation

  • Liu He & Qi-Lin Wang & Ching-Feng Wen & Xiao-Yan Zhang & Xiao-Bing Li, 2019. "A Kind of New Higher-Order Mond-Weir Type Duality for Set-Valued Optimization Problems," Mathematics, MDPI, vol. 7(4), pages 1-18, April.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:4:p:372-:d:225569
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    References listed on IDEAS

    as
    1. Nguyen Anh & Phan Khanh, 2013. "Higher-order optimality conditions in set-valued optimization using radial sets and radial derivatives," Journal of Global Optimization, Springer, vol. 56(2), pages 519-536, June.
    2. 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.
    3. 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.
    4. M. Chinaie & J. Zafarani, 2009. "Image Space Analysis and Scalarization of Multivalued Optimization," Journal of Optimization Theory and Applications, Springer, vol. 142(3), pages 451-467, September.
    5. J. Jahn & A. A. Khan & P. Zeilinger, 2005. "Second-Order Optimality Conditions in Set Optimization," Journal of Optimization Theory and Applications, Springer, vol. 125(2), pages 331-347, May.
    6. Qilin Wang & Guolin Yu, 2011. "Second-Order Optimality Conditions for Set-Valued Optimization Problems Under Benson Proper Efficiency," Abstract and Applied Analysis, Hindawi, vol. 2011, pages 1-16, December.
    Full references (including those not matched with items on IDEAS)

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