MACSYMA experiments with a modified Khachian-type algorithm in linear programming

Abstract

An algorithm of Khachian type for deciding the consistency of m ≥ 2 linear equalities with integer coefficients is described. New iteration formulas for updating the center and the matrix that define each localizing ellipsoid are given. A much sharper bound than that in [1] and [2] for the radius of the initial sphere is given. The new bound depends on the dimension of the solution space, but does <u>not</u> depend explicitly on m. The algorithm is much faster than Khachian's original algorithm. The volume reduction factor in the new algorithm is, in a sense, optimal. Results of computer experiments on the symbolic mathematical system MACSYMA are included.