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

Christian Günther (Christian.Guenthermathematik.uni-halle.de)
Nicolae Popovici (popovicimath.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. 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
Entry Accepted: 07/14/2019
Entry Last Modified: 05/13/2021

Modify/Update this entry