JSIAM Letters
Online ISSN : 1883-0617
Print ISSN : 1883-0609
ISSN-L : 1883-0617
Articles
Numerical Inclusion of Optimum Point for Linear Programming
Shin'ichi OishiKunio Tanabe
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2009 Volume 1 Pages 5-8

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Abstract

This paper concerns with the following linear programming problem: $\mbox{Maximize } c^tx, \mbox{ subject to } Ax \leqq b \mbox{ and } x\geqq 0,$ where $A \in \F^{m\times n}$, $b \in \F^m$ and $c, x \in \F^n$. 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.

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© 2009 The Japan Society for Industrial and Applied Mathematics
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