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Siberian Journal of Numerical Mathematics

2015 year, number 4

An algorithm of the simplex method using a dual basis

Gerard Idelfonovich Zabinyako
Institute of Computational Mathematics and Mathematical Geophysics SB RAS, pr. Lavrentieva, 6, Novosibirsk, 630090
Keywords: LU-разложения, обновление разложений, разреженные матрицы, симплекс-метод, линейное программирование, LU-decomposition, decomposition updating, sparse matrices, simplex method, linear programming

Abstract

An algorithm of the simplex method not requiring an explicit updating of the LU decomposition in iterations is considered. Solutions obtained with fixed LU factors are corrected using small auxiliary matrices. The results of numerical experiments are presented.