The principal aim of this paper is to show that weakly cone-convex vector-valued functions, as well as weakly cone-quasiconvex vector-valued functions, can be characterized in terms of usual weakly convexity and weakly quasiconvexity of certain real-valued functions, defined by means of the extreme directions of the polar cone or by Gerstewitz’s scalarization functions
Scalar characterizations of weakly cone-convex and weakly cone-quasiconvex functions / D. La Torre, N. Popovici, M. Rocca. - In: NONLINEAR ANALYSIS. - ISSN 0362-546X. - 72:3-4(2010 Feb 01), pp. 1909-1915.
Scalar characterizations of weakly cone-convex and weakly cone-quasiconvex functions
D. La TorrePrimo
;
2010
Abstract
The principal aim of this paper is to show that weakly cone-convex vector-valued functions, as well as weakly cone-quasiconvex vector-valued functions, can be characterized in terms of usual weakly convexity and weakly quasiconvexity of certain real-valued functions, defined by means of the extreme directions of the polar cone or by Gerstewitz’s scalarization functions
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