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Existence of weak efficient solutions of set-valued optimization problems

Author

Listed:
  • Fatemeh Fakhar

    (University of Isfahan
    Institute for Research in Fundamental Sciences (IPM))

  • Hamid Reza Hajisharifi

    (University of Isfahan
    Institute for Research in Fundamental Sciences (IPM))

  • Zeinab Soltani

    (University of Kashan)

Abstract

In this paper, we introduce a novel scalarization function for set-valued maps and establish several significant properties that highlight its utility. We extend the concept of regular-global-inf functions, initially studied in the context of single-valued maps, to the realm of set-valued maps. As the first main result, we derive a new Weierstrass-type theorem for set-valued maps satisfying the coercivity condition. Furthermore, utilizing tools from asymptotic analysis, we present an existence theorem for strict weakly l-efficient solutions of set optimization problems under certain non-coercive conditions. To underscore the relevance and applicability of our findings, we provide several corollaries and illustrative examples.

Suggested Citation

  • Fatemeh Fakhar & Hamid Reza Hajisharifi & Zeinab Soltani, 2025. "Existence of weak efficient solutions of set-valued optimization problems," Journal of Global Optimization, Springer, vol. 91(1), pages 199-215, January.
    • Handle: RePEc:spr:jglopt:v:91:y:2025:i:1:d:10.1007_s10898-024-01431-y
    DOI: 10.1007/s10898-024-01431-y
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    References listed on IDEAS

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    1. F. Fakhar & H. R. Hajisharifi & Z. Soltani, 2023. "Noncoercive and noncontinuous equilibrium problems: existence theorem in infinite-dimensional spaces," Journal of Global Optimization, Springer, vol. 86(4), pages 989-1003, August.
    2. Alfred Auslender, 1996. "Noncoercive Optimization Problems," Mathematics of Operations Research, INFORMS, vol. 21(4), pages 769-782, November.
    3. César Gutiérrez & Rubén López & Vicente Novo, 2014. "Existence and Boundedness of Solutions in Infinite-Dimensional Vector Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 162(2), pages 515-547, August.
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