Laptin Y. Methods of nonsmooth optimization for solving structured problems

The thesis is devoted to research and solve problems arising from the use of modern methods of nonsmooth optimization to solve complex optimization problems. New effective methods of constructing unconstrained optimization problem, which are equivalent to the original problem with the restrictions, have been developed. These methods are based on convex extension of objective functions from the feasible set of the original optimization problem to the whole space of variables. Software implementation of the proposed approaches using -algorithm of Shor showed high efficiency and stability with respect to ill-conditioning problems of a special kind. New methods have been developed to determine the values of the coefficients of exact penalty functions that do not require decision of auxiliary optimization problems. The obtained results allow to overcome considerable difficulties in decomposition schemes over the variables associated with the lack of sub solutions for some values of linking variables. The new model is designed to minimize the empirical risk for the problem of constructing a linear classifier in the case of a linearly inseparable training sample. It is shown that under certain conditions, in the case of linearly inseparable training sample for two classes, the special task of constructing linear classifier is polynomially solvable. The advantage of using sequential binary linear classifiers in the case of many classes is shown. The software is developed that solve the problem of optimal design of complex technical objects in modern thermal power stations. Corresponding software was passed into experimental operation in the "ENERGOPROGRES" CKB in Kharkov.