The numerical efficiency of the method of exact quadratic regularization
Journal Title: Комп’ютерне моделювання: аналіз, управління, оптимізація - Year 2017, Vol 2, Issue 2
Abstract
In this paper we consider methods for solving the multi-extreme problems in Euclidean finite-dimensional space and compare their efficiency at the solution of test problems. Such multi-extreme problems arise at mathematical modeling of various difficult systems in economics and finance, management, technological processes, computer science, design and others. We show that this class of problems contains discrete problems and also problems of solution of nonlinear equations. Recently considerable efforts have been made to find effective methods of solving multi-extreme problems. Nowadays researchers use such methods as: semidefinite programming, methods of branches and bounds, dual, genetic, evolutionary and other methods. Complex testing problems are used for the analysis of the efficiency of offered methods. Test problems of constrained and unconstrained optimization include also complex of applied problems. Numerous experiments prove that known methods find the optimal solution for a limited number of test problems. In this paper we consider the method of exact quadratic regularization. It can be used to transform multi-extreme problems into problems of searching maximum norm of a vector on a convex set. It is a very simple transformation. Such transformation often reduces the initial multiextreme problem to the one-extreme one. For solving the transformed problem we use the primal-dual interior point method and bisection method. These methods allow solving high-dimensional multi-extreme problems. A large number of numerical experiments were performed for checking the efficiency of offered method. By implementing the method of exact quadratic regularization we have obtained better results for most test problems with unknown solutions. Comparative numerous experiments prove the substantial advantage of offered method of exact quadratic regularization over widely used optimization methods
Authors and Affiliations
А. И. Косолап
Keywords
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