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Generalized Convexity of Functions and Generalized Monotonicity of Set-Valued Maps

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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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Authors and Affiliations

  1. Mathématiques, Faculté des Sciences, Université de Pau, CNRS URA 1204, Pau, France

    J.-P. Penot (Professor)

  2. Department of Dynamical Systems, Institute of Mathematics, Bo Ho, Hanoi, Vietnam

    P. H. Quang (Researcher)

Authors
  1. J.-P. Penot
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  2. P. H. Quang
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Penot, JP., Quang, P.H. Generalized Convexity of Functions and Generalized Monotonicity of Set-Valued Maps. Journal of Optimization Theory and Applications 92, 343–356 (1997). https://doi.org/10.1023/A:1022659230603

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  • DOI: https://doi.org/10.1023/A:1022659230603

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