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

Authors:
Konstantinos Dosios;Konstantinos Paparrizos
Affiliations:
Department of Applied Informatics, University of Macedonia, 156 Egnatia Str, P. O. Box 1591, Thessaloniki 54 006, Greece;Department of Applied Informatics, University of Macedonia, 156 Egnatia Str, P. O. Box 1591, Thessaloniki 54 006, Greece
Venue:
Operations Research Letters
Year:
1997

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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.