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Generalized Monotonicity of Subdifferentials and Generalized Convexity |
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| Authors: | Penot J P Sach P H |
| Institution: | (1) Laboratory of Applied Mathematics, University of Pau, Pau, France;(2) Hanoi Institute of Mathematics, Bo Ho, Hanoi, Vietnam |
| Abstract: | Characterizations of convexity and quasiconvexity of lower semicontinuous functions on a Banach space X are presented in terms of the contingent and Fréchet subdifferentials. They rely on a general mean-value theorem for such subdifferentials, which is valid in a class of spaces which contains the class of Asplund spaces. |
| Keywords: | Convexity generalized convexity monotone functions pseudoconvexity pseudomonotone functions quasiconvexity quasimonotone functions subdifferentials |
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