A bump triangular dynamic factorization algorithm for the simplex method

A dynamic factorization algorithm is developed which algebraically partitions the basis inverse in such a manner so that the simplex method can be executed from a series of small inverses and the basis itself. This partition is maintained dynamically so that the additional memory required to represent the basis inverse reduces to this series of small inverses for in-core implementations.The algorithm is intended for use in solving general large-scale linear programming problems. This new method of basis representation should permit rather large problems to be solved completely in-core.Preliminary computational experience is presented and comparisons are made with Reid's sparsity-exploiting variant of the Bartels—Golub decomposition for linear programming bases. The computational experience indicated that a significant reduction in memory requirements can usually be obtained using the dynamic factorization approach with only a slight (up to about 20%) degradation of execution time.This research was supported in part by the Air Force Office of Scientific Research, Air Force System Command, USAF, under AFOSR Contract/Grant Number AFOSR-74-2715.