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On convexity and quasiconvexity of extremal value functions in set optimization

Tobias Gerlach(tobias.gerlach***at***tu-ilmenau.de)
Stefan Rocktäschel(stefan.rocktaeschel***at***tu-ilmenau.de)

Abstract: We study different classes of convex and quasiconvex set-valued maps defined by means of the lower-less order relation and the upper-less order relation. The aim of this paper is to formulate necessary and especially sufficient conditions for the convexity/quasiconvexity of extremal value functions.

Keywords: extremal functions, convex functions; convex set-valued maps; quasiconvex functions; quasiconvex set-valued maps.

Category 1: Convex and Nonsmooth Optimization (Generalized Convexity/Monoticity )


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Entry Submitted: 01/14/2021
Entry Accepted: 01/14/2021
Entry Last Modified: 01/14/2021

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