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.