A modified simplicial algorithm for convex maximization based on an extension of \(\omega \)-subdivision

Journal of Global Optimization volume 71, pages297–311(2018)Cite this article

Abstract

The simplicial algorithm is a popular branch-and-bound approach to the convex maximization problem with multiple local maxima. In this paper, we discuss some difficulties revealed when implementing this algorithm under the \(\omega \)-subdivision rule. To overcome those, we modify the bounding process and extend the \(\omega \)-subdivision rule. We also report numerical results for the simplicial algorithm according to the new subdivision rule.

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Acknowledgements

The author would like to thank the anonymous referees for their valuable comments, which significantly improved the readability of this article.

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Affiliations

  1. Graduate School of Systems and Information Engineering, University of Tsukuba, Tsukuba, Ibaraki, 305-8573, Japan

    Takahito Kuno

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  1. Takahito Kuno
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Correspondence to Takahito Kuno.

Additional information

The author was partly supported by a Grant-in-Aid for Scientific Research (C) 16K0028 from Japan Society for the Promotion of Science.

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Kuno, T. A modified simplicial algorithm for convex maximization based on an extension of \(\omega \)-subdivision. J Glob Optim 71, 297–311 (2018). https://doi.org/10.1007/s10898-018-0619-0

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Keywords

  • Global optimization
  • Convex maximization
  • Branch-and-bound
  • Simplicial algorithm
  • \(\omega \)-Subdivision