Abstract. Three classes of methods for generating of pseudorandom sequences based on arithmetic principles are given. A class of matrix nondifferentiable optimization problems is analyzed and a method to solve them based on r-algorithms is proposed. The application is given. Tabl.: 3. Refs: 34 titles.

Keywords: nondifferentiable optimization, stochastic approximation of a random process, uniform distribution with prescribed density, r-algorithm, matrix optimization.