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Scalar characterizations of weakly cone-convex and weakly cone-quasiconvex functions

✍ Scribed by Davide La Torre; Nicolae Popovici; Matteo Rocca

Publisher: Elsevier Science
Year: 2010
Tongue: English
Weight: 470 KB
Volume: 72
Category: Article
ISSN: 0362-546X
DOI: 10.1016/j.na.2009.09.031

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✦ Synopsis

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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