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Network Optimization pp 103–126Cite as

ɛ-Relaxation and Auction Methods for Separable Convex Cost Network Flow Problems

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Part of the book series: Lecture Notes in Economics and Mathematical Systems ((LNE,volume 450))

Abstract

We consider a generic auction method for the solution of the single commodity, separable convex cost network flow problem. This method provides a unifying framework for the ∈-relaxation method and the auction/sequential shortest path algorithm and, as a consequence, we develop a unified complexity analysis for the two methods. We also present computational results showing that these methods are much faster than earlier relaxation methods, particularly for ill-conditioned problems.

This work supported by National Science Foundation, Grant Nos. DMI-9300494 and 9311621

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Author information

Authors and Affiliations

  1. Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, Room 35-210, Cambridge, MA, 02139, UK

    Dimitri P. Bertsekas

  2. IBM T. J. Watson Research Center, Room 23-116C, Yorktown Heights, NY, 10598, USA

    Lakis C. Polymenakos

  3. Department of Mathematics, University of Washington, Seattle, WA, 98195, USA

    Paul Tseng

Authors
  1. Dimitri P. Bertsekas
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  2. Lakis C. Polymenakos
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  3. Paul Tseng
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Editor information

Editors and Affiliations

  1. Center for Applied Optimization ISE Department, University of Florida, 303 Weil Hall, Gainesville, FL, 32611, USA

    Panos M. Pardalos  & Donald W. Hearn  & 

  2. Math Department, University of Florida, Gainesville, FL, 32611, USA

    William W. Hager

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© 1997 Springer-Verlag Berlin Heidelberg

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Bertsekas, D.P., Polymenakos, L.C., Tseng, P. (1997). ɛ-Relaxation and Auction Methods for Separable Convex Cost Network Flow Problems. In: Pardalos, P.M., Hearn, D.W., Hager, W.W. (eds) Network Optimization. Lecture Notes in Economics and Mathematical Systems, vol 450. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-59179-2_6

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  • DOI: https://doi.org/10.1007/978-3-642-59179-2_6

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-62541-4

  • Online ISBN: 978-3-642-59179-2

  • eBook Packages: Springer Book Archive

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