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Open AccessArticle

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

by Elisabeth Köbis 1,*,†, Markus A. Köbis 2,† and Xiaolong Qin 3,†
1
Institute of Mathematics, Faculty of Natural Sciences II, Martin-Luther-University Halle-Wittenberg, 06120 Halle, Germany
2
Department of Mathematics and Computer Science, Institute of Mathematics, Free University Berlin, 14195 Berlin, Germany
3
General Education Center, National Yunlin University of Science and Technology, Douliou 64002, Taiwan
*
Author to whom correspondence should be addressed.
These authors contributed equally to this work.
Mathematics 2020, 8(1), 143; https://doi.org/10.3390/math8010143
Received: 29 October 2019 / Revised: 9 December 2019 / Accepted: 10 January 2020 / Published: 20 January 2020
(This article belongs to the Special Issue Applied Functional Analysis and Its Applications)
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. View Full-Text
Keywords: set optimization; set relations; nonlinear scalarizing functional; algebraic interior; vector closure set optimization; set relations; nonlinear scalarizing functional; algebraic interior; vector closure
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Köbis, E.; Köbis, M.A.; Qin, X. An Inequality Approach to Approximate Solutions of Set Optimization Problems in Real Linear Spaces. Mathematics 2020, 8, 143.

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