Resolution of the problem of degeneracy in a primal and dual simplex algorithm

Abstract

We resolve the problem of degeneracy in a recently developed primal-dual simplex algorithm for general linear programming problems (Chen et al., 1994). We show that the algorithm cycles. It is also shown that if ties are broken by an arbitrary cycling-free pivot rule of the classical primal simplex algorithm, then the refined primal-dual algorithm does not cycle. Exponential worst-case behaviour is shown and relations with other algorithms are discussed.