Year: 1991
Author: Yi-Yong Nie, Shu-Rong Xu
Journal of Computational Mathematics, Vol. 9 (1991), Iss. 3 : pp. 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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/1991-JCM-9400
Journal of Computational Mathematics, Vol. 9 (1991), Iss. 3 : pp. 262–272
Published online: 1991-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 11