Research on mathematical programming.

Abstract

Unified solving method for mathematical programming problems in Euclid space is developed. The method is based on sequential narrowing of admissible solutions set and oriented on using of modern computers. Results of investigation for a general problem of linear programming, convex programming problem and nonlinear programming problem are considered separately. Necessary and sufficient conditions of solution existence for mathematical programming problem are obtained for mentioned problems separately by reducing of given problem to equivalent problem with bounded below target function.Minimizing sequences such that accumulation point of them are solutions for general problem of linear programming, convex programming problem and nonlinear programming problem are constructed. Estimates of the convergence rates are obtained. Solving of examples by developed method using is adduced. The scientific value of obtained results is the method is applicable to both confluent and nonsingular mathematical programming problems: it is not necessary to find an extreme point and to go on to the next point, which leads to circularity in most cases; convex programming problem and nonlinear programming problem solving are not related to finding saddle value of Lagrange function, saddle value existence conditions are not necessary. Developing of new effective solution methods for mathematical programming problems is topical for solving of economics, natural sciences, engineering and information technologies problems.