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Weak minimal elements and weak minimal solutions of a nonconvex set-valued optimization problem

Author

Listed:
  • M. Chinaie

    (University of Isfahan)

  • F. Fakhar

    (University of Isfahan)

  • M. Fakhar

    (University of Isfahan
    Institute for Research in Fundamental Sciences)

  • H. R. Hajisharifi

    (University of Khansar
    Institute for Research in Fundamental Sciences)

Abstract

In this paper, we characterize the nonemptiness of the set of weak minimal elements for a nonempty subset of a linear space. Moreover, we obtain some existence results for a nonconvex set-valued optimization problem under weaker topological conditions.

Suggested Citation

  • M. Chinaie & F. Fakhar & M. Fakhar & H. R. Hajisharifi, 2019. "Weak minimal elements and weak minimal solutions of a nonconvex set-valued optimization problem," Journal of Global Optimization, Springer, vol. 75(1), pages 131-141, September.
    • Handle: RePEc:spr:jglopt:v:75:y:2019:i:1:d:10.1007_s10898-019-00810-0
    DOI: 10.1007/s10898-019-00810-0
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    References listed on IDEAS

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    1. Petra Weidner, 2017. "Gerstewitz Functionals on Linear Spaces and Functionals with Uniform Sublevel Sets," Journal of Optimization Theory and Applications, Springer, vol. 173(3), pages 812-827, June.
    2. Adan, M. & Novo, V., 2003. "Weak efficiency in vector optimization using a closure of algebraic type under cone-convexlikeness," European Journal of Operational Research, Elsevier, vol. 149(3), pages 641-653, September.
    3. M. Adán & V. Novo, 2004. "Proper Efficiency in Vector Optimization on Real Linear Spaces," Journal of Optimization Theory and Applications, Springer, vol. 121(3), pages 515-540, 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. Chuang-Liang Zhang & Nan-jing Huang, 2021. "Set Relations and Weak Minimal Solutions for Nonconvex Set Optimization Problems with Applications," Journal of Optimization Theory and Applications, Springer, vol. 190(3), pages 894-914, September.

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