An Inequality Approach to Approximate Solutions of Set Optimization Problems in Real Linear Spaces

Elisabeth Köbis, Markus A. Köbis and Xiaolong Qin
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Elisabeth Köbis: Institute of Mathematics, Faculty of Natural Sciences II, Martin-Luther-University Halle-Wittenberg, 06120 Halle, Germany
Markus A. Köbis: Department of Mathematics and Computer Science, Institute of Mathematics, Free University Berlin, 14195 Berlin, Germany
Xiaolong Qin: General Education Center, National Yunlin University of Science and Technology, Douliou 64002, Taiwan

Mathematics, 2020, vol. 8, issue 1, 1-17

Abstract: This paper explores new notions of approximate minimality in set optimization using a set approach. We propose characterizations of several approximate minimal elements of families of sets in real linear spaces by means of general functionals, which can be unified in an inequality approach. As particular cases, we investigate the use of the prominent Tammer–Weidner nonlinear scalarizing functionals, without assuming any topology, in our context. We also derive numerical methods to obtain approximate minimal elements of families of finitely many sets by means of our obtained results.

Keywords: set optimization; set relations; nonlinear scalarizing functional; algebraic interior; vector closure (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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