Abstract
Let ℝn be then-dimensional real Euclidean space,x=(x 1,x 2, ...,x n)T ∈ ℝn, and letf:ℝn → R be a real-valued function. We consider the problem of finding the global minimizers off. A new method to compute numerically the global minimizers by following the paths of a system of stochastic differential equations is proposed. This method is motivated by quantum mechanics. Some numerical experience on a set of test problems is presented. The method compares favorably with other existing methods for global optimization.
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Communicated by R. A. Tapia
This research has been supported by the European Research Office of the US Army under Contract No. DAJA-37-81-C-0740.
The third author gratefully acknowledges Prof. A. Rinnooy Kan for bringing to his attention Ref. 4.
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Aluffi-Pentini, F., Parisi, V. & Zirilli, F. Global optimization and stochastic differential equations. J Optim Theory Appl 47, 1–16 (1985). https://doi.org/10.1007/BF00941312
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DOI: https://doi.org/10.1007/BF00941312