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| Paper IPM / M / 18004 |
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| Abstract: | |||||
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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 regularglobal-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.
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