Stovba V. Subgradient method with Polyak's step in transformed space

The thesis is devoted to the study of subgradient method with Polyak’s step modifications with scalar parameter and space transformation operation for finding a minimum point of ravine convex functions with optimal value known. The main attention is paid to the question of convergence and convergence rate of the modifications proposed. In particular, in the thesis monotonous decrease of distance to the minimum point is proved and convergence rate parameters are given of the subgradient method with Polyak’s step modifications proposed in original and transformed space of variables for arbitrary convex functions and convex functions with acute minimum. Program implementations of all of the proposed modifications of subgradient method with Polyak’s step are developed in C++ and the number of computational experiments are conducted for minimization of smooth and non-smooth ravine convex functions using the modifications proposed. For the first time the ellipsoid method algorithm is built for solving linear regression parameters determination problem with arbitrary value of parameter p. Algorithm based on Yudin-Nemirovskii ellipsoid method is proposed for finding solutions of linear equation system with two-sided constraints on variables.