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Global optimization and stochastic differential equations. (English) Zbl 0549.65038
Let \({\mathbb{R}}^ n\) be the n-dimensional real Euclidean space, \(x=(x_ 1,x_ 2,...,x_ n)^{T}\in {\mathbb{R}}^ n\), and let f: \({\mathbb{R}}^ n\to {\mathbb{R}}\) be a real-valued function. We consider the problem of finding the global minimizers of f. 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.

MSC:
65K05 Numerical mathematical programming methods
90C30 Nonlinear programming
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
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