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

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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.

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Authors and Affiliations

  1. Institute for Mathematics, Technische Universität Ilmenau, Ilmenau, Germany

    Gabriele Eichfelder

  2. Faculty of Mathematics and Computer Science, Technische Universität Bergakademie Freiberg, Freiberg, Germany

    Maria Pilecka

Authors
  1. Gabriele Eichfelder
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  2. Maria Pilecka
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Correspondence to Gabriele Eichfelder.

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Communicated by Nguyen Dong Yen.

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Eichfelder, G., Pilecka, M. Set Approach for Set Optimization with Variable Ordering Structures Part I: Set Relations and Relationship to Vector Approach. J Optim Theory Appl 171, 931–946 (2016). https://doi.org/10.1007/s10957-016-0992-0

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  • DOI: https://doi.org/10.1007/s10957-016-0992-0

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