Set Approach for Set Optimization with Variable Ordering Structures Part II: Scalarization Approaches

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 10, 947-963

Abstract: Abstract This paper combines variable ordering structures with set relations in set optimization. We continue our examinations of set optimization problems and use the optimality notions as well as the set relations introduced in the paper (Eichfelder and Pilecka in Set Approach for Set Optimization with Variable Ordering Structures Part I: Set Relations and Relationship to Vector Approach, 2016). We present linear scalarization results and a new nonlinear scalarization approach for set relations. Moreover, we introduce some additional set relations which allow us to investigate connections between our results, based on the set approach, and others presented in the literature which are based on the vector approach. This gives us the possibility to apply the optimality conditions derived there to our concepts.

Keywords: Set optimization; Set relation; Variable ordering structure; Scalarization; 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/s10957-016-0993-z

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