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Convexification and Concavification for a General Class of Global Optimization Problems

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Abstract

A kind of general convexification and concavification methods is proposed for solving some classes of global optimization problems with certain monotone properties. It is shown that these minimization problems can be transformed into equivalent concave minimization problem or reverse convex programming problem or canonical D.C. programming problem by using the proposed convexification and concavification schemes. The existing algorithms then can be used to find the global solutions of the transformed problems.

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Authors and Affiliations

  1. Department of Mathematics and Computer Science, Chongqing Normal University, Chongqing, 400047, China

    Z. Y. Wu

  2. Department of Mathematics, Shanghai University, Baoshan, Shanghai, 200436, P.R. China

    Z. Y. Wu & L. S. Zhang

  3. Institute of Mathematics, Fudan University, Shanghai, 200433, P.R. China

    F. S. Bai

Authors
  1. Z. Y. Wu
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  2. F. S. Bai
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  3. L. S. Zhang
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Correspondence to Z. Y. Wu.

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Wu, Z.Y., Bai, F.S. & Zhang, L.S. Convexification and Concavification for a General Class of Global Optimization Problems. J Glob Optim 31, 45–60 (2005). https://doi.org/10.1007/s10898-004-0569-6

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  • DOI: https://doi.org/10.1007/s10898-004-0569-6

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