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Volume 3, Issue 3, 31 December 2021, Pages 325-340
Abstract. In this paper, we investigate very general scalarization concepts for solving set-valued optimization problems where the pre-order is induced by the upper set-less relation as introduced by Kuroiwa. The scalarization functionals that we consider in the analysis are not given explicitly, but are rather general functions that satisfy certain properties, such as monotonicity, separation, transitivity, translation invariance, and the transfer of inclusion. Underlined by several examples, we show how certain combinations of such properties can be used to characterize the set relation by simple inequalities. We further propose a derivative-free descent method based on our theoretical findings.
How to Cite this Article:
Elisabeth Köbis, Markus A. Köbis, Characterizing the upper set relation by general functionals, Appl. Set-Valued Anal. Optim. 3 (2021), 325-340.