Existence of weak efficient solutions of set-valued optimization problems

Fatemeh Fakhar (), Hamid Reza Hajisharifi () and Zeinab Soltani ()
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Fatemeh Fakhar: University of Isfahan
Hamid Reza Hajisharifi: University of Isfahan
Zeinab Soltani: University of Kashan

Journal of Global Optimization, 2025, vol. 91, issue 1, No 8, 199-215

Abstract: 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.

Keywords: Set optimization problem; Coercivity condition; Noncoercivity condition; Asymptotic function; 49J53; 90C26; 90C29; 90C48 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s10898-024-01431-y

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