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Subvexormal Functions and Subvex Functions

Author

Listed:
  • X. F. Li

    (Jilin University of Technology)

  • J. L. Dong

    (Jilin University of Technology)

Abstract

Subvexormal functions and subinvexormal functions are proposed, whose properties are shared commonly by most generalized convex functions and most generalized invex functions, respectively. A necessary and sufficient condition for a subvexormal function to be subinvexormal is given in the locally Lipschitz and regular case. Furthermore, subvex functions and subinvex functions are introduced. It is proved that the class of strictly subvex functions is equivalent to that of functions whose local minima are global and that, in the locally Lipschitz and regular case, both strongly subvex functions and strongly subinvex functions can be characterized as functions whose relatively stationary points (slight extension of stationary points) are global minima.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:103:y:1999:i:3:d:10.1023_a:1021744309992
    DOI: 10.1023/A:1021744309992
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    References listed on IDEAS

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    1. Zang, I. & Choo, E.U. & Avriel, M., 1977. "On functions whose stationary points are global minima," LIDAM Reprints CORE 308, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    2. Jean-Philippe Vial, 1983. "Strong and Weak Convexity of Sets and Functions," Mathematics of Operations Research, INFORMS, vol. 8(2), pages 231-259, May.
    3. VIAL, Jean-Philippe, 1983. "Strong and weak convexity of sets and functions," LIDAM Reprints CORE 529, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    4. 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.
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