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Convexification, Concavification and Monotonization in Global Optimization

Author

Listed:
  • D. Li
  • X.L. Sun
  • M.P. Biswal
  • F. Gao

Abstract

We show in this paper that via certain convexification, concavification and monotonization schemes a nonconvex optimization problem over a simplex can be always converted into an equivalent better-structured nonconvex optimization problem, e.g., a concave optimization problem or a D.C. programming problem, thus facilitating the search of a global optimum by using the existing methods in concave minimization and D.C. programming. We first prove that a monotone optimization problem (with a monotone objective function and monotone constraints) can be transformed into a concave minimization problem over a convex set or a D.C. programming problem via pth power transformation. We then prove that a class of nonconvex minimization problems can be always reduced to a monotone optimization problem, thus a concave minimization problem or a D.C. programming problem. Copyright Kluwer Academic Publishers 2001

Suggested Citation

  • 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.
    • Handle: RePEc:spr:annopr:v:105:y:2001:i:1:p:213-226:10.1023/a:1013313901854
    DOI: 10.1023/A:1013313901854
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    Cited by:

    1. Fatima Bellahcene, 2019. "Application of the polyblock method to special integer chance constrained problem," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 29(4), pages 23-40.
    2. 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.
    3. So Yeon Chun & Miguel A. Lejeune, 2020. "Risk-Based Loan Pricing: Portfolio Optimization Approach with Marginal Risk Contribution," Management Science, INFORMS, vol. 66(8), pages 3735-3753, August.

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