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Convexification of Nonsmooth Monotone Functions1

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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.

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Author information

Authors and Affiliations

  1. Department of Management Science, School of Management, Fudan University, 670 Guoshun Road, Shanghai, 200433, China

    X. L. Sun (Professor)

  2. Department of Mathematics, Shanghai University, Baoshan, Shanghai, China

    H. Z. Luo (PhD Candidate)

  3. Department of Applied Mathematics, Zhejiang University of Technology, Hangzhou, Zhejiang, China

    H. Z. Luo (PhD Candidate)

  4. Department of Systems Engineering and Engineering Management, Chinese University of Hong Kong, Shatin, New Territories, Hong Kong

    D. Li (Professor)

Authors
  1. X. L. Sun
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  2. H. Z. Luo
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  3. D. Li
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Additional information

Communicated by X. Q. Yang

This research was partially supported by the National Natural Science Foundation of China under Grants 70671064 and 60473097 and by the Research Grants Council of Hong Kong under Grant CUHK 4214/01E.

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Sun, X.L., Luo, H.Z. & Li, D. Convexification of Nonsmooth Monotone Functions1 . J Optim Theory Appl 132, 339–351 (2007). https://doi.org/10.1007/s10957-006-9160-2

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  • DOI: https://doi.org/10.1007/s10957-006-9160-2

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