We propose an extension of the ε-relaxation method to generalized network flow problems with separable convex cost. The method maintains ε-complementary slackness satisfied at all iterations and adjusts the arc flows and the node prices so to satisfy flow conservation upon termination. Each iteration of the method involves either a price change at a node or a flow change at an arc or a flow change around 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/ε), where ε0 and ε denote, respectively, the initial and the final ε.
CITATION STYLE
Tseng, P., & Bertsekas, D. P. (1996). An ε-Relaxation method for generalized separable convex cost network flow problems. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 1084, pp. 85–93). Springer Verlag. https://doi.org/10.1007/3-540-61310-2_7
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