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Lipschitz B-Vex Functions and Nonsmooth Programming

Author

Listed:
  • X. F. Li

    (Jilin University of Technology)

  • J. L. Dong

    (Jilin University of Technology)

  • Q. H. Liu

    (Jilin University of Technology)

Abstract

In this paper, the equivalence between the class of B-vex functions and that of quasiconvex functions is proved. Necessary and sufficient conditions, under which a locally Lipschitz function is B-vex, are established in terms of the Clarke subdifferential. Regularity of locally Lipschitz B-vex functions is discussed. Furthermore, under appropriate conditions, a necessary optimality condition of the Slater type and a sufficient optimality condition are obtained for a nonsmooth programming problem involving B-vex functions.

Suggested Citation

  • X. F. Li & J. L. Dong & Q. H. Liu, 1997. "Lipschitz B-Vex Functions and Nonsmooth Programming," Journal of Optimization Theory and Applications, Springer, vol. 93(3), pages 557-574, June.
    • Handle: RePEc:spr:joptap:v:93:y:1997:i:3:d:10.1023_a:1022643129733
    DOI: 10.1023/A:1022643129733
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    Cited by:

    1. Vsevolod Ivanov, 2013. "Characterizations of pseudoconvex functions and semistrictly quasiconvex ones," Journal of Global Optimization, Springer, vol. 57(3), pages 677-693, November.
    2. X. F. Li & J. L. Dong, 1999. "Subvexormal Functions and Subvex Functions," Journal of Optimization Theory and Applications, Springer, vol. 103(3), pages 675-704, December.

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