Abstract
We consider the minimum cost network flow problem and describe how the non-linear penalty function methods of Conn and Bartels can be specialized to a combinatorial algorithm for this problem. We report on preliminary computational results which show that this method can require fewer pivots than the simplex method while the amount of work required for each pivot is comparable. The algorithm can be proven finite using a modification of Cunningham's strongly feasible basis pivoting rule.
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Supported by the Natural Sciences and Engineering Research Council of Canada, and the joint research project “Combinatorial Optimization” of the Natural Sciences and Engineering Research Council, Canada and the German Research Association (Deutsche Forschungsgemeinschaft, SFB 303).
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Gamble, A.B., Conn, A.R. & Pulleyblank, W.R. A network penalty method. Mathematical Programming 50, 53–73 (1991). https://doi.org/10.1007/BF01594924
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DOI: https://doi.org/10.1007/BF01594924