Decision methods for some discrete extreme problems in recognition theory

By optimizing different models of recognition algorithms, a number of discrete extreme problems appear. The search for the maximum solvable subsystem of the system of linear inequalities is one of these tasks. The solution algorithm for this problem is described. This algorithm is effective for linear systems of small ranks. Also, an approximate method that is effective for systems of large dimensionality is proposed. The text was submitted by the author in English. Natalja N. Katerinochkina. Born 1945. Graduated from the Faculty of Mechanics and Mathematics, Moscow State University, in 1967. Received candidates degree in Physics and Mathematics in 1978. The senior scientific worker at the Dorodnicyn Computing Centre, Russian Academy of Science. Scientific interests: discrete mathematics, mathematical cybernetics, pattern recognition, discrete optimization. Author of 35 publications.