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Generalized Monotonicity of Subdifferentials and Generalized Convexity

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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.

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Authors and Affiliations

  1. Laboratory of Applied Mathematics, University of Pau, Pau, France

    J. P. Penot (Professor)

  2. Hanoi Institute of Mathematics, Bo Ho, Hanoi, Vietnam

    P. H. Sach (Professor)

Authors
  1. J. P. Penot
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  2. P. H. Sach
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Penot, J.P., Sach, P.H. Generalized Monotonicity of Subdifferentials and Generalized Convexity. Journal of Optimization Theory and Applications 94, 251–262 (1997). https://doi.org/10.1023/A:1022628223741

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  • DOI: https://doi.org/10.1023/A:1022628223741

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