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The Bundle Method for Hard Combinatorial Optimization Problems

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Combinatorial Optimization — Eureka, You Shrink!

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2570))

Abstract

Solving the well known relaxations for large scale combinatorial optimization problems directly is out of reach. We use Lagrangian relaxations and solve it with the bundle method. The cutting plane model at each iteration which approximates the original problem can be kept moderately small and we can solve it very quickly. We report successful numerical results for approximating maximum cut.

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Author information

Authors and Affiliations

  1. Carinthia Tech Institute, School of Geoinformation, A-9524, Villach, Austria

    Gerald Gruber

  2. Department of Mathematics, University of Klagenfurt, A-9020, Klagenfurt, Austria

    Franz Rendl

Authors
  1. Gerald Gruber
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  2. Franz Rendl
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Editor information

Editors and Affiliations

  1. Institut für Informatik, Universität zu Köln, Pohligstr. 1, 50969, Köln, Germany

    Michael Jünger

  2. Institut für Informatik, Universität Heidelberg, Im Neuenheimer Feld 368, 69120, Heidelberg, Germany

    Gerhard Reinelt

  3. Istituto di Analisi dei Sistemi ed Informatica “Antonio Ruberti”, CNR, viale Manzoni 30, 00185, Rome, Italy

    Giovanni Rinaldi

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Gruber, G., Rendl, F. (2003). The Bundle Method for Hard Combinatorial Optimization Problems. In: Jünger, M., Reinelt, G., Rinaldi, G. (eds) Combinatorial Optimization — Eureka, You Shrink!. Lecture Notes in Computer Science, vol 2570. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-36478-1_9

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  • DOI: https://doi.org/10.1007/3-540-36478-1_9

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-00580-3

  • Online ISBN: 978-3-540-36478-8

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