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International Symposium on Systems Optimization and Analysis pp 210–224Cite as

Algorithms for nonlinear multicommodity network flow problems

  • Numerical Methods In Optimization
  • Conference paper
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Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 14))

Abstract

This paper presents a class of algorithms for optimization of convex multi-commodity flow problems. The algorithms are based on the ideas of Gallager's methods for distributed optimization of delay in data communication networks [1],

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References

  1. Gallager, R., "A Minimum Delay Routing Algorithm Using Distributed Computation," IEEE Trans. on Communication, vol. COM-25, 1974, pp. 73–85.

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  2. Gallager, R., "Scale Factors for Distributed Routing Algorithms," Paper ESL-P-770, Electronic Systems Lab., Massachusetts Institute of Technology, Cambridge, Mass., August 1977.

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  3. Goldstein, A. A., "Convex Programming in Hilbert Space," Bull. Amer. Math. Soc., Vol. 70, 1964, pp. 709–710.

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  4. Levitin, E. S. and B. T. Polyak, "Constrained Minimization Problems," USSR Comput. Math. Math. Phys., Vol. 6, 1966, pp. 1–50.

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  5. Bertsekas, D. P., "Algorithms for Optimal Routing of Flow in Networks," Coordinated Science Lab., University of Illinois, Urbana, Ill., June 1978.

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  6. Daniel, J. W., The Approximate Minimization of Functionals, Prentice-Hall, Englewood Cliffs, N.J., 1971.

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  7. Polak, E., Computational Methods in Optimization: A Unified Approach, Academic Press, N.Y., 1971.

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  8. Bertsekas, D. P., "On the Goldstein-Levitin-Polyak Gradient Projection Method," IEEE Transactions on Automatic Control, Vol. AC-21, 1976, pp. 174–184.

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  9. Bertsekas, D. P., E. Gafni, and K. Vastola, "Validation of Algorithms for Optimal Routing of Flow in Networks," Proc. of IEEE Conf. on Decision and Control, San Diego, Calif., January 1979.

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Author information

Authors and Affiliations

  1. Coordinated Science Laboratory, University of Illinois, 61801, Urbana, Illinois, USA

    Dimitri P. Bertsekas

Authors
  1. Dimitri P. Bertsekas
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Editor information

A. Bensoussan J. L. Lions

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© 1979 Springer-Verlag

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Bertsekas, D.P. (1979). Algorithms for nonlinear multicommodity network flow problems. In: Bensoussan, A., Lions, J.L. (eds) International Symposium on Systems Optimization and Analysis. Lecture Notes in Control and Information Sciences, vol 14. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0002656

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  • DOI: https://doi.org/10.1007/BFb0002656

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-09447-0

  • Online ISBN: 978-3-540-35232-7

  • eBook Packages: Springer Book Archive

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