Set Approach for Set Optimization with Variable Ordering Structures Part I: Set Relations and Relationship to Vector Approach

Gabriele Eichfelder () and Maria Pilecka ()
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Gabriele Eichfelder: Technische Universität Ilmenau
Maria Pilecka: Technische Universität Bergakademie Freiberg

Journal of Optimization Theory and Applications, 2016, vol. 171, issue 3, No 9, 946 pages

Abstract: Abstract This paper aims at combining variable ordering structures with set relations in set optimization, which have been defined using the constant ordering cone before. We provide several new set relations in the context of variable ordering structures, discuss their usefulness, and give different examples from a practical point of view. After analyzing the properties of the introduced relations, we define solution notions for set-valued optimization problems equipped with variable ordering structures. We also relate these new notions to those ones obtained by the so-called vector approach.

Keywords: Set optimization; Set relation; Variable ordering structure; 49J53; 90C29; 90C30; 54C60 (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (3)

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DOI: 10.1007/s10957-016-0992-0

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