Global optimization and stochastic differential equations

Let ℝn be then-dimensional real Euclidean space,x=(x1,x2, ...,xn)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.