A modified simplicial algorithm for convex maximization based on an extension of \(\omega \)-subdivision
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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.
KeywordsGlobal optimization Convex maximization Branch-and-bound Simplicial algorithm \(\omega \)-Subdivision
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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