Abstract.
We present combinatorial interior point methods for the generalized minimum cost flow and the generalized circulation problems based on Wallacher and Zimmermann's combinatorial interior point method for the minimum cost network flow problem. The algorithms have features of both a combinatorial algorithm and an interior point method. They work towards optimality by iteratively reducing the value of a potential function while maintaining interior point solutions. At each iteration, flow is augmented along a generalized circulation, which is computed by solving a TVPI (Two Variables Per Inequality) system. The algorithms run in time, where m and n are, respectively, the number of arcs and nodes in the graph, and L is the length of the input data.
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Received: June 1, 2001 / Accepted: May 23, 2002-08-22 Published online: September 27, 2002
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ID="*" This research was supported in part by NSF Grants DMS 94-14438, DMS 95-27124, CDA 97-26385 and DMS 01-04282, and DOE Grant DE-FG02-92ER25126
Mathematics Subject Classification (2000): 20E28, 20G40, 20C20
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Goldfarb, D., Lin, Y. Combinatorial interior point methods for generalized network flow problems. Math. Program., Ser. A 93, 227–246 (2002). https://doi.org/10.1007/s10107-002-0333-y
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DOI: https://doi.org/10.1007/s10107-002-0333-y