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Open Mathematics

formerly Central European Journal of Mathematics

Editor-in-Chief: Gianazza, Ugo / Vespri, Vincenzo

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2391-5455
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Volume 3, Issue 2

Issues

Volume 13 (2015)

Exact and stable least squares solution to the linear programming problem

Evald Übi
Published Online: 2005-06-01 | DOI: https://doi.org/10.2478/BF02479198

Abstract

A linear programming problem is transformed to the finding an element of polyhedron with the minimal norm. According to A. Cline [6], the problem is equivalent to the least squares problem on positive ortant. An orthogonal method for solving the problem is used. This method was presented earlier by the author and it is based on the highly developed least squares technique. First of all, the method is meant for solving unstable and degenerate problems. A new version of the artifical basis method (M-method) is presented. Also, the solving of linear inequality systems is considered.

Keywords: Linear programming; method of least squares; M-method

Keywords: 90C05; 65K05

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  • [2] E. Übi: “On Computing a Stable Least Squares Solution to the Linear Programming Problem”, Proc. Estonian Acad. Sci. Phys. Math., Vol 47, (1998), pp. 251–259. Google Scholar

  • [3] E. Übi: “Finding Non-negative Solution of Overdetermined or Underdetermined System of Linear Equations by Method of Least Squares”, Trans. Tallinn Tech. Univ., Vol. 738, (1994), pp. 61–68. Google Scholar

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  • [5] A. Cline: “An Elimination Method for the Solution of Linear Least Squares Problems”, SIAM J. Numer. Anal., Vol. 10, (1973), pp. 283–289. http://dx.doi.org/10.1137/0710027Google Scholar

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  • [8] T. Hu: Integer programming and Network flows, Addison-Wesley Publishing Company, Massachusetts, 1970. Google Scholar

About the article

Published Online: 2005-06-01

Published in Print: 2005-06-01


Citation Information: Open Mathematics, Volume 3, Issue 2, Pages 228–241, ISSN (Online) 2391-5455, DOI: https://doi.org/10.2478/BF02479198.

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© 2005 Versita Warsaw. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

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[1]
E. Übi
Central European Journal of Mathematics, 2008, Volume 6, Number 1, Page 171
[2]
Evald Übi
Central European Journal of Mathematics, 2007, Volume 5, Number 2, Page 373

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