Characterizations of generalized convexities via generalized directional derivatives |
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| Authors: | Pham Huu Sach Jean-Paul Penot |
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| Affiliation: | 1. Hanoi Institute of Matematics , P.O. Box 631, Boho , Hanoi , Vietnam;2. Laboratoire de Mathématiques Appliquées, , Université de Pau et des Pays de 1'Adour , Avenue de l'Université , PAU , 64000 , France |
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| Abstract: | The paper gives characterizations of convexity, quasiconvexity, invexity and pseudoconvexity for a (radially) upper-semicontinuous function f in a topological vector space via appropriate properties of a bifunction which is majorized by the upper radial derivative of f and which stands for a generalized derivative of some sort. |
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| Keywords: | convexity derivatives generalized convexity generalized derivatives invexity monotone mapping pseudo-convexity quasiconvexity, quasimonotone operator |
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