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The Method of Exterior Forms in Linear Programming

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Abstract:

The method of exterior forms by H. Grassmann and E. Cartan is used for solving the linear programming problem. It captures the essence of the problem in a convenient, compact form. The solution is presented by Cramer’s like rules and is reduced to computing the set of values of the objective function at the vertices of the polyhedron constraints, without any explicit calculation of the vertices themselves.

Info:

Periodical:
Bulletin of Mathematical Sciences and Applications (Volume 14)
Pages:
7-12
Citation:
G. V. Kondratiev "The Method of Exterior Forms in Linear Programming", Bulletin of Mathematical Sciences and Applications, Vol. 14, pp. 7-12, 2016
Online since:
February 2016
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References:

[1] G. B. Dantzig, Linear Programming and Extensions, Princeton University Press, (1963).

[2] I. Maros, Computational Techniques of the Simplex Method, Springer Science+Business Media, New York, (2003).

[3] B. A. Murtagh, Advanced Linear Programming: Computation and Practice, McGraw-Hill International Book Company, (1981).

[4] H. Grassmann, Die Ausdehnungslehre. Vollständig und in strenger Form begründet., Berlin: Enslin, 1862.

DOI: https://doi.org/10.1017/cbo9781107325081.003

[5] E. Cartan, Les systèmes différentiels extérieurs et leurs applications géométriques, Hermann, (1945).

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