An ε-Relaxation method for generalized separable convex cost network flow problems

  • Paul Tseng
  • Dimitri P. Bertsekas
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1084)


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.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1996

Authors and Affiliations

  • Paul Tseng
    • 1
  • Dimitri P. Bertsekas
    • 2
  1. 1.Department of MathematicsUniversity of WashingtonSeattleUSA
  2. 2.Department of Electrical Engineering and Computer ScienceMassachusetts Institute of TechnologyCambridgeUSA

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