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Generalized Monotonicity of Subdifferentials and Generalized Convexity

Author

Listed:
  • J. P. Penot

    (University of Pau)

  • P. H. Sach

    (Hanoi Institute of Mathematics)

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.

Suggested Citation

  • J. P. Penot & P. H. Sach, 1997. "Generalized Monotonicity of Subdifferentials and Generalized Convexity," Journal of Optimization Theory and Applications, Springer, vol. 94(1), pages 251-262, July.
    • Handle: RePEc:spr:joptap:v:94:y:1997:i:1:d:10.1023_a:1022628223741
    DOI: 10.1023/A:1022628223741
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    References listed on IDEAS

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    1. Correa Romar, 2014. "Mathematical Foci," Mathematical Economics Letters, De Gruyter, vol. 2(1-2), pages 5-11, August.
    2. J. P. Penot, 1997. "Mean-Value Theorem with Small Subdifferentials," Journal of Optimization Theory and Applications, Springer, vol. 94(1), pages 209-221, July.
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    Cited by:

    1. J. Dutta & S. Chandra, 2002. "Convexifactors, Generalized Convexity, and Optimality Conditions," Journal of Optimization Theory and Applications, Springer, vol. 113(1), pages 41-64, April.
    2. J. P. Penot, 1997. "Mean-Value Theorem with Small Subdifferentials," Journal of Optimization Theory and Applications, Springer, vol. 94(1), pages 209-221, July.

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