Abstract.
We generalize the ε-relaxation method of [14] for the single commodity, linear or separable convex cost network flow problem to network flow problems with positive gains. The method maintains ε-complementary slackness at all iterations and adjusts the arc flows and the node prices so as to satisfy flow conservation upon termination. Each iteration of the method involves either a price change on a node or a flow change along an arc or a flow change along a simple cycle. Complexity bounds for the method are derived. For one implementation employing ε-scaling, the bound is polynomial in the number of nodes N, the number of arcs A, a certain constant Γ depending on the arc gains, and ln(ε0/), where ε0 and denote, respectively, the initial and the final tolerance ε.
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Received: November 10, 1996 / Accepted: October 1999¶Published online April 20, 2000
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Tseng, P., Bertsekas, D. An ε-relaxation method for separable convex cost generalized network flow problems. Math. Program. 88, 85–104 (2000). https://doi.org/10.1007/PL00011379
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DOI: https://doi.org/10.1007/PL00011379