Transformation of co-ordinates to the problems of global optimization

Abstract

Actuality. We consider a problem of global optimization in Euclidian  finite-dimensional space. Such problems arise at mathematical modelling of difficult systems in the technician, management, economy, technological processes, designing, an artificial intellect, computer science and other fields of knowledge. These problems belong to the class NP-difficult. Effective numerical methods are not developed for such problems yet. Purpose. We use transformation of space and exact quadratic regularization for the numerical solution of problems of global optimization. Research methods. We use a method exact quadratic regularization for the solution of multiextreme problems. It is a method reduces the problem solution to a maximum of norm of a vector on convex set. We offer transformation of co-ordinates which consists in displacement of admissible area in a direction of a bisector positive orthant. It raises numerical efficiency of a method exact quadratic regularization in problems of global optimization. Results. Displacement of co-ordinates often leads an initial multiextreme problem of the one-extreme. We use an effective is primer-dual interior point method  for the solution of the received problem. Generally, it is necessary to use also a dichotomy method. Conclusions. The new technique is developed for the solution of multiextreme problems. Comparative numerical experiments confirm efficiency of the given transformation at the solution of set of test problems of global optimization. The given technique has shown the best numerical results in comparison with the numerical results received by the best existing methods. We have received the best results practically for all known test problems of global optimization. This technique can be used for the solution of difficult applied problems.