CEJM 3(2) 2005 228–241 Exact and stable least squares solution to the linear programming problem Evald ¨ Ubi ∗ Department of Economics, Tallinn University of Technology, Kopli 101, 11712 Tallinn, Estonia Received 29 March 2004; accepted 20 September 2004 Abstract: A linear programming problem is transformed to the finding an element of polyhedron with the minimal norm. According to A.Cline [6], the problem is equivalent to the least squares problem on positive ortant. An orthogonal method for solving the problem is used. This method was presented earlier by the author and it is based on the highly developed least squares technique. First of all, the method is meant for solving unstable and degenerate problems. A new version of the artifical basis method (M-method) is presented. Also, the solving of linear inequality systems is considered. c  Central European Science Journals. All rights reserved. Keywords: Linear programming, method of least squares, M-method MSC (2000): 90C05, 65K05 1 Introduction The least squares method is used in mechanics, physics, statistics, but not in linear programming. The application of this universal method in mathematical programming is the main purpose of this paper. We consider the standard linear program min{z =(c, x)}, s.t.Ax = b, x ≥ 0 (1) * E-mail: evaldy@tv.ttu.ee