On Auxiliary Algorithm for the Simplex Method by H. Luh and R. Tsaih

Abstract

The interesting auxiliary algorithm for simplex method by Luh and Tsaih (Computers and Operations Research 29 (2002)) and its modified version by B. J. Chaderjian and T. Gao (Computers and Operations Research 30 (2003)) present an effective method to start an initial basic feasible solution from an interior feasible solution. We modify the algorithm in the above reference. By using QR decomposition, a much smaller (n–m–k)×(n–m–k) matrix, in stead of a n×n matrix, is handled in k ^th iteration. The QR factors at each iteration can be obtained from its predecessor cheaply by an updating process. This substantially improve the efficiency of the algorithm proposed by Luh and Tsaih.