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Efficient Dual Methods for Nonlinearly Constrained Networks

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Computational Science and Its Applications – ICCSA 2005 (ICCSA 2005)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3483))

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Abstract

The minimization of nonlinearly constrained network flow problems can be performed by exploiting the efficiency of the network flow techniques. It lies in minimizing approximately a series of (augmented) Lagrangian functions including only the side constraints, subject to balance constraints in the nodes and capacity bounds. One of the drawbacks of the multiplier methods with quadratic penalty function when is applied to problems with inequality constraints is that the corresponding augmented Lagrangian function is not twice continuously differentiable even if the cost and constraint functions are. The author’s purpose is to put forward two methods that overcome this difficulty: the exponential multiplier method and the ε-subgradient method, and to compare their efficiency with that of the quadratic multiplier method and that of the codes MINOS and LOQO. The results are encouraging.

The research was partially supported by grant MCYT DPI 2002-03330.

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Author information

Authors and Affiliations

  1. Department of Applied Mathematics and, Statistics and Operations Research, University of the Basque Country, P.O. Box 644, 48080, Bilbao, Spain

    Eugenio Mijangos

Authors
  1. Eugenio Mijangos
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Editor information

Editors and Affiliations

  1. Department of Mathematics and Computer Science, University of Perugia, via Vanvitelli, 1, I-06123, Perugia, Italy

    Osvaldo Gervasi

  2. Department of Computer Science, University of Calgary, 2500 University Drive N.W., T2N 1N4, Calgary, AB, Canada

    Marina L. Gavrilova

  3. William Norris Professor, Head of the Computer Science and Engineering Department, University of Minnesota, USA

    Vipin Kumar

  4. Department of Chemistry, University of Perugia, Via Elce di Sotto, 8, I-06123, Perugia, Italy

    Antonio Laganá

  5. Institute of High Performance Computing, IHCP, 1 Science Park Road, 01-01 The Capricorn, Singapore Science Park II, 117528, Singapore

    Heow Pueh Lee

  6. School of Computing, Soongsil University, Seoul, Korea

    Youngsong Mun

  7. Clayton School of IT, Monash University, 3800, Clayton, Australia

    David Taniar

  8. OptimaNumerics Ltd, Belfast, United Kingdom

    Chih Jeng Kenneth Tan

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© 2005 Springer-Verlag Berlin Heidelberg

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Mijangos, E. (2005). Efficient Dual Methods for Nonlinearly Constrained Networks. In: Gervasi, O., et al. Computational Science and Its Applications – ICCSA 2005. ICCSA 2005. Lecture Notes in Computer Science, vol 3483. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11424925_51

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  • DOI: https://doi.org/10.1007/11424925_51

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-25863-6

  • Online ISBN: 978-3-540-32309-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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