A least-squares primal-dual algorithm for solving linear programming problems

Authors:
Earl Barnes;Victoria Chen;Balaji Gopalakrishnan;Ellis. L. Johnson
Affiliations:
School of Industrial & Systems Engineering, Georgia Institute of Technology, Atlanta, GA 30332, USA;School of Industrial & Systems Engineering, Georgia Institute of Technology, Atlanta, GA 30332, USA;School of Industrial & Systems Engineering, Georgia Institute of Technology, Atlanta, GA 30332, USA;School of Industrial & Systems Engineering, Georgia Institute of Technology, Atlanta, GA 30332, USA
Venue:
Operations Research Letters
Year:
2002

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Abstract

We have developed a least-squares primal-dual algorithm for solving linear programming problems that is impervious to degeneracy, with strict improvement attained at each iteration. We tested our algorithm on a range of linear programming problems including ones that require many pivots, usually because of degeneracy, using the primal simplex method and the dual simplex method with steepest edge pivoting. On average, our algorithm took less than half the number of iterations required by the primal and dual simplex methods; on some problems, it took over 30 times fewer iterations.