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Characterizations of explicitly quasiconvex vector functions w.r.t. polyhedral cones
Christian Günther (Christian.Guenther 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. Günther 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 Download: [PDF] Entry Submitted: 07/14/2019 Modify/Update this entry | ||
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