A dual method for optimal routing in packet-switched networks

  • Cassilda Ribeiro
  • Didier El Baz
II Mathematical Programming II.2 Discrete Optimization
Part of the Lecture Notes in Control and Information Sciences book series (LNCIS, volume 180)


Dual Method Network Flow Problem Broyden Fletcher Goldfarb Shanno Main Node Multicommodity Flow 
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  1. [AUT 87]
    G. Authie, Contribution à l’optimisation de flots dans les réseaux. Un multiprocesseur expérimental pour l’étude des itérations asynchrones, Thèse de Doctorat d’Etat, UPS Toulouse, 1987.Google Scholar
  2. [BEE 87]
    D. P. Bertsekas and D. El Baz, Distributed asynchronous relaxation methods for convex network flow problems, SIAM J. on Cont. and Opt., 25 (1987), pp. 74–85.zbMATHCrossRefGoogle Scholar
  3. [BEG 83]
    D. P. Bertsekas and M. Gafni, Projected Newton methods and optimization of multicommodity flows, IEEE Trans. Automat. Control, 28 (1983) pp. 1090–1096.zbMATHCrossRefMathSciNetGoogle Scholar
  4. [BEG 87]
    D. P. Bertsekas and R. Gallager, Data Networks, Prentice Hall, Englewood Cliffs, N. J., 1987.Google Scholar
  5. [BET 89]
    D. P. Bertsekas and J. Tsitsiklis, Parallel and Distributed Computation, Prentice Hall, Englewood Cliffs, N. J., 1989.zbMATHGoogle Scholar
  6. [BUC 90]
    R. Buckers, Numerical experiments with dual algorithm for partially separable nonlinear optimization problems, Proceedings of the Parallel Computing 89 Conference, D. Evans et al. eds, Elsevier Science Publishing, North Holland, 1990, p. 555–562.Google Scholar
  7. [CHM 88]
    R. Chen and R. Meyer, Parallel optimization for traffic assignment, Mathematical Programming, Series B 42 (1988), pp. 327–346.zbMATHCrossRefMathSciNetGoogle Scholar
  8. [DEM 77]
    J. Dennis and J. Moré, Quasi-Newton methods, motivation and theory, SIAM Review, 19 (1977), pp. 46–88.zbMATHCrossRefMathSciNetGoogle Scholar
  9. [DES 83]
    R. Dembo and T. Steihaug, Truncated-Newton algorithms for large-scale unconstrained optimization, Mathematical Programming, 26 (1983), pp. 190–212.zbMATHCrossRefMathSciNetGoogle Scholar
  10. [FGK 73]
    L. Fratta, M. Gerla and L. Kleinrock, The flow deviation method: an approach to store-and-forward communication network design, Networks, 3, (1973), pp. 97–133.CrossRefMathSciNetGoogle Scholar
  11. [FLE 74]
    R. Fletcher, Methods related to Lagrangian functions, in Numerical Methods for Constrained Optimization, Gill and Murray eds, Academic Press, London, (1974), pp. 219–239.Google Scholar
  12. [KLE 64]
    L. Kleinrock, Communication Nets: Stochastic Message Flow and Delay, McGraw-Hill, New York, 1964.Google Scholar
  13. [KLE 76]
    L. Kleinrock, Queuing Systems, John Wiley, New York, 1976.Google Scholar
  14. [LOO 90]
    F. Lootsma, Exploitation of structure in nonlinear optimization, Proceedings of the Parallel computing 89 Conference, D. J. Evans et al. editors, Elsevier Science Publishing B. V. North Holland, 1990, p. 31–45.Google Scholar
  15. [MIN 83]
    M. Minoux, Programmation Mathématique, Dunod, Paris, 1983.zbMATHGoogle Scholar
  16. [NAS 89]
    S. Nash and A. Sofer, Block truncated Newton methods for parallel optimization, Mathematical Programming, 45 (1989), pp. 529–546.zbMATHCrossRefMathSciNetGoogle Scholar
  17. [ROC 70]
    R. Rockafellar, Convex Analysis, Princeton University Press, Princeton, 1970.zbMATHGoogle Scholar
  18. [ROC 84]
    R. Rockafellar, Network Flows and Monotropic Optimization, John Wiley & Sons, New York, 1984.zbMATHGoogle Scholar
  19. [SCC 75]
    M. Schwartz and C. Cheung, The gradient projection algorithm for multiple routing in message-switched networks, Proc. Fourth annual Data Communications Symposium, Oct. 7–9 1975, Quebec city, Canada.Google Scholar
  20. [STE 77]
    T. Stern, A class of decentralized routing algorithms using relaxation, IEEE Trans. on Communications, COM 25 (1977), pp. 1092–1102.CrossRefGoogle Scholar
  21. [YOU 71]
    D. Young, Iterative solution of large linear systems, Academic Press, New York, 1971.zbMATHGoogle Scholar

Copyright information

© International Federation for Information Processing 1992

Authors and Affiliations

  • Cassilda Ribeiro
    • 1
  • Didier El Baz
    • 1
  1. 1.LAAS du CNRSToulouse CedexFrance

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