A Characterization of Quasiconvex Vector-valued Functions

@inproceedings{Benoist2002ACO,
  title={A Characterization of Quasiconvex Vector-valued Functions},
  author={Jo{\"e}l Benoist and Jonathan M. Borwein and Nicolae Popovici},
  year={2002}
}
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 wellknown 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 Rn. 

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