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Convexification of Nonsmooth Monotone Functions1

Author

Listed:
  • X. L. Sun

    (Fudan University)

  • H. Z. Luo

    (Shanghai University
    Zhejiang University of Technology)

  • D. Li

    (Chinese University of Hong Kong)

Abstract

We consider a convexification method for a class of nonsmooth monotone functions. Specifically, we prove that a semismooth monotone function can be converted into a convex function via certain convexification transformations. The results derived in this paper lay a theoretical base to extend the reach of convexification methods in monotone optimization to nonsmooth situations.

Suggested Citation

  • X. L. Sun & H. Z. Luo & D. Li, 2007. "Convexification of Nonsmooth Monotone Functions1," Journal of Optimization Theory and Applications, Springer, vol. 132(2), pages 339-351, February.
    • Handle: RePEc:spr:joptap:v:132:y:2007:i:2:d:10.1007_s10957-006-9160-2
    DOI: 10.1007/s10957-006-9160-2
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    References listed on IDEAS

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    1. Siegfried Schaible, 1976. "Fractional Programming. I, Duality," Management Science, INFORMS, vol. 22(8), pages 858-867, April.
    2. Horst, R., 1984. "On the convexification of nonlinear programming problems: An applications-oriented survey," European Journal of Operational Research, Elsevier, vol. 15(3), pages 382-392, March.
    3. D. Li & X.L. Sun & M.P. Biswal & F. Gao, 2001. "Convexification, Concavification and Monotonization in Global Optimization," Annals of Operations Research, Springer, vol. 105(1), pages 213-226, July.
    4. Schaible, Siegfried, 1981. "Fractional programming: Applications and algorithms," European Journal of Operational Research, Elsevier, vol. 7(2), pages 111-120, June.
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    Cited by:

    1. Hezhi Luo & Huixian Wu & Jianzhen Liu, 2013. "Some Results on Augmented Lagrangians in Constrained Global Optimization via Image Space Analysis," Journal of Optimization Theory and Applications, Springer, vol. 159(2), pages 360-385, November.

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