The authors consider a global minimum problem in \(\mathbb{R}^ n\) with finite numbers of both equality and inequality constraints \(h_ i(x)\leq 0\) and \(h_ i(x)= 0\), where the objective function \(F\) and all \(h_ i\) are \(C^ 2\). The problem is solved by considering the unconstrained problem, but with a penalty term that is multiplied by a penalty parameter and added to \(F\). Under a certain growth assumption a sequence of such problems with increasing penalty parameter produces a sequence of their global minima, the cluster points of which are global minima of the original constrained problem. The constrained problems are solved using the fact that their global minimum coincides with the global maximum of the asymptotic density of a solution to a stochastic integral (or differential) equation that is simulated by an implicit one-step method representing a local minimization overlayed by Gaussian increments (random search). After a fixed number of steps the result is refined by non-stochastic local minimization. The method is implemented in parallel on a transputer network, and numerical results are presented.