A generalized scalarization method in set optimization with respect to variable domination structures / E. Köbis, L. Th. Tam and Chr. Tammer
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A generalized scalarization method in set optimization with respect to variable domination structures
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894994646
URN
urn:nbn:de:gbv:3:2-75333
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Publication history
Halle/Saale : Martin-Luther-Universität Halle-Wittenberg, Naturwissenschaftliche Fakultät II, Institut für Mathematik, [2017]
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1 Online-Ressource (35 Seiten, 362 KB) : Diagramme
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ger
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Abstract
In this paper, we introduce new nonlinear scalarization methods to characterize minimal elements of set-valued problems equipped with variable domination structures. For certain set relations with respect to variable domination structures, we give a characterization of these relations using corresponding nonlinear scalarizing functionals and the properties of these functionals. We describe different kinds of minimal elements to a family of sets with respect to variable domination structures. Furthermore, we investigate a descent method to find approximations of minimal solutions of set-valued problems with respect to variable domination structures using nonlinear scalarization methods. Finally, we apply the results to a set-valued problem in Medical Image Registration.
Series
Reports ; 2017, No. 07 ppn:584754027