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Relaxation Methods for Linear Programs

Paul Tseng and Dimitri P. Bertsekas
Mathematics of Operations Research
Vol. 12, No. 4 (Nov., 1987), pp. 569-596
Published by: INFORMS
Stable URL: http://www.jstor.org/stable/3689919
Page Count: 28
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Relaxation Methods for Linear Programs
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Abstract

In this paper we propose a new method for solving linear programs. This method may be viewed as a generalized coordinate descent method whereby the descent directions are chosen from a finite set. The generation of the descent directions are based on results from monotropic programming theory. The method may be alternatively viewed as an extension of the relaxation method for network flow problems [1], [2]. Node labeling, cuts, and flow augmentation paths in the network case correspond to, respectively, tableau pivoting, rows of tableaus, and columns of tableaus possessing special sign patterns in the linear programming case.

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