Volume 9, Issue 3
An Isometric Plane Method for Linear Programming

J. Comp. Math., 9 (1991), pp. 262-272.

Published online: 1991-09

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• Abstract

In this paper the following canonical form of a general LP problem, $${\rm max} \ Z=C^TX,$$
$${\rm subject} \ {\rm to} \ AX\geq b$$is considered for $X\in R^n$. The constraints form an arbitrary convex polyhedron $\Omega^m$ in $R^n$. In $\Omega^m$ a strictly interior point is successively moved to a higher isometric plane from a lower one along the gradient function value maximum is found or the infinite value of the objective function is concluded. For an $m\ast n$ matrix $A$ the arithmetic operations of a movement are $O(mn)$ in our algorithm. The algorithm enables one to solve linear equations with ill conditions as well as a general LP problem. Some interesting examples illustrate the efficiency of the algorithm.

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@Article{JCM-9-262, author = {Nie , Yi-Yong and Xu , Shu-Rong}, title = {An Isometric Plane Method for Linear Programming}, journal = {Journal of Computational Mathematics}, year = {1991}, volume = {9}, number = {3}, pages = {262--272}, abstract = {

In this paper the following canonical form of a general LP problem, $${\rm max} \ Z=C^TX,$$
$${\rm subject} \ {\rm to} \ AX\geq b$$is considered for $X\in R^n$. The constraints form an arbitrary convex polyhedron $\Omega^m$ in $R^n$. In $\Omega^m$ a strictly interior point is successively moved to a higher isometric plane from a lower one along the gradient function value maximum is found or the infinite value of the objective function is concluded. For an $m\ast n$ matrix $A$ the arithmetic operations of a movement are $O(mn)$ in our algorithm. The algorithm enables one to solve linear equations with ill conditions as well as a general LP problem. Some interesting examples illustrate the efficiency of the algorithm.

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/9400.html} }
TY - JOUR T1 - An Isometric Plane Method for Linear Programming AU - Nie , Yi-Yong AU - Xu , Shu-Rong JO - Journal of Computational Mathematics VL - 3 SP - 262 EP - 272 PY - 1991 DA - 1991/09 SN - 9 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/9400.html KW - AB -

In this paper the following canonical form of a general LP problem, $${\rm max} \ Z=C^TX,$$
$${\rm subject} \ {\rm to} \ AX\geq b$$is considered for $X\in R^n$. The constraints form an arbitrary convex polyhedron $\Omega^m$ in $R^n$. In $\Omega^m$ a strictly interior point is successively moved to a higher isometric plane from a lower one along the gradient function value maximum is found or the infinite value of the objective function is concluded. For an $m\ast n$ matrix $A$ the arithmetic operations of a movement are $O(mn)$ in our algorithm. The algorithm enables one to solve linear equations with ill conditions as well as a general LP problem. Some interesting examples illustrate the efficiency of the algorithm.

Yi-Yong Nie & Shu-Rong Xu. (1970). An Isometric Plane Method for Linear Programming. Journal of Computational Mathematics. 9 (3). 262-272. doi:
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