A convergent simplicial algorithm with [omega]-subdivision and [omega]-bisection strategies

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)....

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Bibliographic Details
Published inJournal of global optimization Vol. 52; no. 3; p. 371
Main Authors Kuno, Takahito, Buckland, Paul E; K
Format Journal Article
LanguageEnglish
Published Dordrecht Springer Nature B.V 01.03.2012
Subjects
Algorithms
Integer programming
Linear programming
Optimization
Studies
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Summary: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.[PUBLICATION ABSTRACT]
ISSN:0925-5001
1573-2916
DOI:10.1007/s10898-011-9746-6