Optimal (in the Sense of the Minimum of the Polyhedral Norm) Matrix Correction of Inconsistent Systems of Linear Algebraic Equations and Improper Linear Programming Problems in Interval Constraints

Abstract

The problems of multiparameter (matrix) correction of the inconsistent systems of the linear algebraic equations and improper linear programming problems written down in a canonical form have been considered in this paper. Optimum criteria pointed out in the given problems are the weighted minimax criterion and the minimum of the considered sum of the absolute values of the elements of matrix correction requirement. The considered problems of correction are supplemented with interval constraints put in over the corrected elements of the matrix system and its right part. The analyzed systems of the linear algebraic equations can contain fixed (not subject to correction) rows and columns. Calculating layouts of the solution of the stated problems of matrix correction are given and substantiated. The calculating layouts demand the minimum of the scalar positive parameters on the upper (external) level and reduced to the solution of the dependent on the stated parameter of the systems of the linear algebraic equations and inequalities and also the problems of linear programming on the low (internal) level.