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Diffusions for global optimization. (English) Zbl 0602.60071
This paper describes a problem of finding a global minimum of a real- valued function defined on the unit hypercube in Euclidean n-space. The problem is changed to a stochastic differential equation by using the gradient of the above function as the drift term and a diffusion term which is interpreted as a constant times the square root of ”temperature”.
Under suitable conditions this diffusion converges weakly to a Gibbs distribution. If these Gibbs distributions have a unique weak limit as the temperature approaches zero then for a certain temperature function the diffusion converges weakly to this weak limit of the Gibbs distributions which has its support on the global minima of the original function.
Reviewer: T.Duncan

MSC:
60J60 Diffusion processes
60J70 Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.)
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