POINTWISE RESIDUAL METHOD FOR SOLVING PRIMAL AND DUAL ILL-POSED LINEAR PROGRAMMING PROBLEMS WITH APPROXIMATE DATA

Abstract

Abstract We propose a variation of the pointwise residual method for solving primal and dual ill-posed linear programming with approximate data, sensitive to small perturbations. The method leads to an auxiliary problem, which is also a linear programming problem. Theorems of existence and convergence of approximate solutions are established and optimal estimates of approximation of initial problem solutions are achieved.