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Volume 5, Issue 5, 1 October 2021, Pages 721-735
Abstract. Optimization of set-valued mappings has become an important subbranch of optimization. In set optimization, one of the main tools to compare sets is given by set relations, which are binary relations among sets. The main two set relations known in the literature are the upper and lower set relation, which are somewhat counterparts of each other and are used to model robust and optimistic solutions in uncertain (vector) programming, respectively. In this paper, we consider the convex case and propose a new set relation which is able to act as a weighting function between these two important set relations and therefore balances out possible gaps that can occur in modeling set optimization problems.
How to Cite this Article:
Elisabeth Köbis, Markus Arthur Köbis, The weighted set relation: Characterizations in the convex case, J. Nonlinear Var. Anal. 5 (2021), 721-735.