Exact and stable least squares solution to the linear programming problem

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.