A convergent simplicial algorithm with ω-subdivision and ω-bisection strategies

Authors:
Takahito Kuno;Paul E. Buckland
Affiliations:
Graduate School of Systems and Information Engineering, University of Tsukuba, Tsukuba, Ibaraki, Japan 305-8573;Graduate School of Systems and Information Engineering, University of Tsukuba, Tsukuba, Ibaraki, Japan 305-8573 and Genesis Power Limited, Auckland, New Zealand
Venue:
Journal of Global Optimization
Year:
2012

Citing 5
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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 驴-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.