A Characterization of Quasiconvex Vector-Valued Functions

Borwein, Jonathan M. and Benoist, Joel and Popovici, Nicolae (2002) A Characterization of Quasiconvex Vector-Valued Functions. Proceedings of the American Mathematical Society, 131 . pp. 1109-1113. ISSN 0002-9939

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      The aim of this paper is to characterize in terms of scalar quasiconvexity the vector-valued functions which are $K$-quasiconvex with respect to a closed convex cone $K$ in a Banach space. Our main result extends a well-known characterization of $K$-quasiconvexity by means of extreme directions of the polar cone of $K$, obtained by Dinh The Luc in the particular case when $K$ is a polyhedral cone generated by exactly $n$ linearly independent vectors in the Euclidean space $\R^n$.

      Item Type: Article
      Additional Information: pubdom FALSE
      Uncontrolled Keywords: quasiconvex vector-valued functions,scalarization,polar cones
      Subjects: 90-xx Economics, operations research, programming, games > 90Cxx Mathematical programming
      26-xx Real functions > 26Bxx Functions of several variables
      Faculty: UNSPECIFIED
      Depositing User: Users 1 not found.
      Date Deposited: 24 Nov 2003
      Last Modified: 13 Jan 2015 11:50

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