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Characterizations of explicitly quasiconvex vector functions w.r.t. polyhedral cones

Christian GŁnther (Christian.Guenther***at***mathematik.uni-halle.de)
Nicolae Popovici (popovici***at***math.ubbcluj.ro)

Abstract: The aim of this paper is to present new characterizations of explicitly cone-quasiconvex vector functions with respect to a polyhedral cone of a finite-dimensional Euclidean space. These characterizations are given in terms of classical explicit quasiconvexity of certain real-valued functions, defined by composing the vector-valued function with appropriate scalarization functions, namely the extreme directions of the polar cone or some nonlinear scalarization functions, currently used in vector optimization.

Keywords: Generalized convex vector functions; polyhedral cones; extreme directions; nonlinear scalarization function

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

Citation: C. GŁnther and N. Popovici: Characterizations of explicitly quasiconvex vector functions w.r.t. polyhedral cones. Journal of Nonlinear and Convex Analysis 20(12):2653-2665, 2019

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Entry Submitted: 07/14/2019
Entry Accepted: 07/14/2019
Entry Last Modified: 05/13/2021

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