Generalized Convexity of Functions and Generalized Monotonicity of Set-Valued Maps |
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Authors: | Penot J-P Quang P H |
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Institution: | (1) Mathématiques, Faculté des Sciences, Université de Pau, CNRS URA 1204, Pau, France;(2) Department of Dynamical Systems, Institute of Mathematics, Bo Ho, Hanoi, Vietnam |
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Abstract: | We establish connections between some concepts of generalized monotonicity for set-valued maps introduced earlier and some notions of generalized convexity. Moreover, a notion of pseudomonotonicity for set-valued maps is introduced; it is shown that, if a function f is continuous, then its pseudoconvexity is equivalent to the pseudomonotonicity of its generalized subdifferential in the sense of Clarke and Rockafellar. |
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Keywords: | Quasiconvex functions pseudoconvex functions invex functions quasimonotone maps pseudomonotone maps generalized subdifferentials |
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