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Sequential characterizations of approximate solutions in convex vector optimization problems with set-valued maps

Author

Listed:
  • Nithirat Sisarat

    (Naresuan University)

  • Rabian Wangkeeree

    (Naresuan University
    Naresuan University)

  • Tamaki Tanaka

    (Niigata University)

Abstract

This paper deals with a convex vector optimization problem with set-valued maps. In the absence of constraint qualifications, it provides, by the scalarization theorem, sequential Lagrange multiplier conditions characterizing approximate weak Pareto optimal solutions for the problem in terms of the approximate subdifferentials of the marginal function associated with corresponding set-valued maps. The paper shows also that this result yields the approximate Lagrange multiplier condition for the problem under a new constraint qualification which is weaker than the Slater-type constraint qualification. Illustrative examples are also provided to discuss the significance of the sequential conditions.

Suggested Citation

  • Nithirat Sisarat & Rabian Wangkeeree & Tamaki Tanaka, 2020. "Sequential characterizations of approximate solutions in convex vector optimization problems with set-valued maps," Journal of Global Optimization, Springer, vol. 77(2), pages 273-287, June.
    • Handle: RePEc:spr:jglopt:v:77:y:2020:i:2:d:10.1007_s10898-019-00864-0
    DOI: 10.1007/s10898-019-00864-0
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    References listed on IDEAS

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    2. Taiyong Li & Yihong Xu & Chuanxi Zhu, 2007. "∊-Strictly Efficient Solutions Of Vector Optimization Problems With Set-Valued Maps," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 24(06), pages 841-854.
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    4. J.M. Martínez & B.F. Svaiter, 2003. "A Practical Optimality Condition Without Constraint Qualifications for Nonlinear Programming," Journal of Optimization Theory and Applications, Springer, vol. 118(1), pages 117-133, July.
    5. J. Baier & J. Jahn, 1999. "On Subdifferentials of Set-Valued Maps," Journal of Optimization Theory and Applications, Springer, vol. 100(1), pages 233-240, January.
    6. 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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    Cited by:

    1. L. Q. Anh & T. Q. Duy & D. V. Hien, 2020. "Stability of efficient solutions to set optimization problems," Journal of Global Optimization, Springer, vol. 78(3), pages 563-580, November.
    2. Mohamed Laghdir & El Mahjoub. Echchaabaoui, 2023. "Sequential Pareto Subdifferential Sum Rule for Convex Set-Valued Mappings and Applications," Journal of Optimization Theory and Applications, Springer, vol. 198(3), pages 1226-1245, September.

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