Multidimensional Constrained Global Optimization in Domains with Computable Boundaries

Abstract

Multidimensional constrained global optimization problem with objective function under Lipschitz condition and constraints generating a feasible domain with computable boundaries is considered. For solving this problem the dimensionality reduction approach on the base of the nested optimization scheme is used. This scheme reduces initial multidimensional problem to a family of one-dimensional subproblems and allows applying univariate methods for the execution of multidimensional optimization. Sequential and parallel modifications of well-known information-statistical methods of Lipschitz optimization are proposed for solving the univariate subproblems arising inside the nested scheme in the case of domains with computable boundaries. A comparison with classical penalty function method being traditional means of taking into account the constraints is carried out. The results of experiments demonstrate a significant advantage of the methods proposed over the penalty function method.