Scalarization Functionals with Uniform Level Sets in Set Optimization

Truong Quang Bao () and Christiane Tammer ()
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Truong Quang Bao: Northern Michigan University
Christiane Tammer: Martin-Luther-University Halle-Wittenberg

Journal of Optimization Theory and Applications, 2019, vol. 182, issue 1, No 13, 310-335

Abstract: Abstract We use the original form of Gerstewitz’s nonlinear scalarization functional to characterize upper and lower set-less minimizers of set-valued maps acting from a nonempty set into a real linear space with respect to the lower (resp. upper) set-less relation introduced by Kuroiwa. Our main results are as follows: An upper set-less minimizer to a set-valued map (with respect to the image space) is an upper set-less minimal solution to a scalarization of the set-valued map (with respect to the space of real numbers), where the hypergraphical multifunction is involved in the scalarization and vice versa, a lower set-less minimizer to a set-valued map (with respect to the image space) is an upper set-less minimal solution to an appropriate scalarization of the set-valued map (in the space of real numbers), where the epigraphical multifunction is involved in the scalarization and vice versa, and a lower set-less minimizer to a set-valued map becomes a (Pareto) minimizer to the same map provided that the map enjoys a domination property.

Keywords: Nonlinear scalarization functional; Set optimization; Set-less relations; Scalarization characteristics; 49J53; 65K10; 90C26 (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s10957-019-01504-z

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