Kosolap A. Development of the determined models and methods of global optimization with convexity use

This thesis is devoted to working out the theory and methods of searching out points of a global minimum in multiextreme problems. We offer a new section of global optimization - superconvex optimization for which is defined a canonical form and the method of relaxation cuttings is developed. We show big attention to a new direction in research of difficult systems - semidefinite optimization for which we develop the generalized simplex-method. The new direction in global optimization opens a method of a quadratic regularization which divided multiextreme problems into two classes of complexity. The transformed сonvex problems concern the first class, and the second class is formed by problems of maximization of norm square of a vector on a convex set. We offer the scheme of piecewise-linear modeling for dynamic problems of performance of difficult projects. We consider new models of market economy. We realise all offered methods and algorithms in a software package Excel_SP the with the built in programming language. We have made considerable numerical experiments on offered methods and algorithms which testify to their advantages to the solution of difficult multiextreme problems