A centering by the monte-carlo method

The maximization of Gaussian probability of the multidimensional set is considered, when expectations of Gaussian distribution are varying and the co-variance matrix is fixed. It is shown that the necessary condition of maximum is a centering, i.e. the optimal point coincides with the weight center of the set. Iterative methods for solving this problem are developed: the analytical centering procedure and the stochastic one by series of Monte-Carlo samples of fixed or regulated size. The convergence of these procedures is considered and the properties of their application in the computer-aided design of systems are discussed