Numerical Inclusion of Optimum Point for Linear Programming

This paper concerns with the following linear programming problem: Maximize ctx, subject to Ax ≦ b and x ≧ 0, where A ∈ Fm×n, b ∈ Fm and c, x ∈ Fn. Here, F is a set of floating point numbers. The aim of this paper is to propose a numerical method of including an optimum point of this linear programming problem provided that a good approximation of an optimum point is given. The proposed method is base on Kantorovich’s theorem and the continuous Newton method. Kantorovich’s theorem is used for proving the existence of a solution for complimentarity equation and the continuous Newton method is used to prove feasibility of that solution. Numerical examples show that a computational cost to include optimum point is about 4 times than that for getting an approximate optimum solution.