Random oscillations arising in the MACSYMA implementation of Khachian-type algorithms in linear programming

Abstract

Anderson and Wang in [1] ran a series of experiments on MACSYMA to test the practicality of the now widely publicized Khachian algorithm for deciding the consistency of a system of linear inequalities. They found the Khachian algorithm to be highly impractical even for very small-sized problems which, in turn, led them to construct a modified algorithm which proved to be a substantial improvement over the original one. In this paper, results of a statistical analysis of data furnished by these experiments are presented. In particular, attention is focussed on the parameter α which in a sense measures, at each step, the saving in using the Anderson-Wang modified algorithm. An intriguing discovery is the fact that α i is a random time series which fluctuates between -1 and 0 before approaching zero as the procedure terminates.Also, it appears that much progress has to be made before such algorithms can be of use in practical problems.