Geodesic
Algorithm for finding of a non-negative solution for linear system of equations
Čelâbinskij fiziko-matematičeskij žurnal, Tome 1 (2016) no. 2, pp. 68-77

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The new algorithm for finding of the exact solution for the linear programming problem is constructed. The method is based on the converting of the linear programming problem to the problem of solving in nonnegative numbers for a system of linear equations with an incomplete rank. This problem is solved by successive approximations in specially constructed subspaces. The convergence of the algorithm for a finite number of the steps is proved. The algorithm has been tested on the data of the Klee–Minty problem and on a set of random tests.
Keywords: algorithm of linear programming, non-negative solution of linear system of equations, linear inequality. 
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     author = {Y. N. Sevostyanov and M. G. Leptchinski},
     title = {Algorithm for finding of a non-negative solution for linear system of equations},
     journal = {\v{C}el\^abinskij fiziko-matemati\v{c}eskij \v{z}urnal},
     pages = {68--77},
     publisher = {mathdoc},
     volume = {1},
     number = {2},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CHFMJ_2016_1_2_a6/}
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Y. N. Sevostyanov; M. G. Leptchinski. Algorithm for finding of a non-negative solution for linear system of equations. Čelâbinskij fiziko-matematičeskij žurnal, Tome 1 (2016) no. 2, pp. 68-77. http://geodesic.mathdoc.fr/item/CHFMJ_2016_1_2_a6/