Abstract
The simplicial algorithm is a kind of branch-and-bound method for computing a globally optimal solution of a convex maximization problem. Its convergence under the ω-subdivision strategy was an open question for some decades until Locatelli and Raber proved it (J Optim Theory Appl 107:69–79, 2000). In this paper, we modify their linear programming relaxation and give a different and simpler proof of the convergence. We also develop a new convergent subdivision strategy, and report numerical results of comparing it with existing strategies.
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Takahito Kuno was partially supported by a Grant-in-Aid for Scientific Research (B 20310082) and a Grant-in-Aid for Challenging Exploratory Research (22651057) from the Japan Society for the Promotion of Sciences.
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Kuno, T., Buckland, P.E.K. A convergent simplicial algorithm with ω-subdivision and ω-bisection strategies. J Glob Optim 52, 371–390 (2012). https://doi.org/10.1007/s10898-011-9746-6
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DOI: https://doi.org/10.1007/s10898-011-9746-6