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

We resolve the problem of degeneracy in a recently developed primal–dual simplex algorithm for general linear programming problems. 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.