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
2012-01-01
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.Pubblicazioni consigliate
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