Pseudomonotone* single–valued functions were introduced in [9] and it was proved that the gradient of a differentiable pseudoconvex function is pseudomonotone*. In the same paper this concept was extended in a natural way to multivalued maps but, to date, there is no result that elates. multivalued pseudomonotone* maps to the subdifferential of locally Lipschitz pseudoconvex functions.. In this paper, we give a nonsmooth Lipschitz pseudoconvex function whose subdifferential is not pseudomonotone* in the sense of [9]. Besides such a characterization was achieved in [10] using a weaker definition of pseudomonotonicity*. Exploiting this weaker concept, we provide a characterization of the solution set of pseudoconvex programs.

A characterization of the solution set of pseudoconvex extremum problems

CASTELLANI, MARCO;GIULI, MASSIMILIANO
2012

Abstract

Pseudomonotone* single–valued functions were introduced in [9] and it was proved that the gradient of a differentiable pseudoconvex function is pseudomonotone*. In the same paper this concept was extended in a natural way to multivalued maps but, to date, there is no result that elates. multivalued pseudomonotone* maps to the subdifferential of locally Lipschitz pseudoconvex functions.. In this paper, we give a nonsmooth Lipschitz pseudoconvex function whose subdifferential is not pseudomonotone* in the sense of [9]. Besides such a characterization was achieved in [10] using a weaker definition of pseudomonotonicity*. Exploiting this weaker concept, we provide a characterization of the solution set of pseudoconvex programs.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11697/89598
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