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A dual method for optimal routing in packet-switched networks

  • II Mathematical Programming
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Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 180))

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References

  1. 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. 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.

    Article  MATH  Google Scholar 

  3. D. P. Bertsekas and M. Gafni, Projected Newton methods and optimization of multicommodity flows, IEEE Trans. Automat. Control, 28 (1983) pp. 1090–1096.

    Article  MATH  MathSciNet  Google Scholar 

  4. D. P. Bertsekas and R. Gallager, Data Networks, Prentice Hall, Englewood Cliffs, N. J., 1987.

    Google Scholar 

  5. D. P. Bertsekas and J. Tsitsiklis, Parallel and Distributed Computation, Prentice Hall, Englewood Cliffs, N. J., 1989.

    MATH  Google Scholar 

  6. 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. R. Chen and R. Meyer, Parallel optimization for traffic assignment, Mathematical Programming, Series B 42 (1988), pp. 327–346.

    Article  MATH  MathSciNet  Google Scholar 

  8. J. Dennis and J. Moré, Quasi-Newton methods, motivation and theory, SIAM Review, 19 (1977), pp. 46–88.

    Article  MATH  MathSciNet  Google Scholar 

  9. R. Dembo and T. Steihaug, Truncated-Newton algorithms for large-scale unconstrained optimization, Mathematical Programming, 26 (1983), pp. 190–212.

    Article  MATH  MathSciNet  Google Scholar 

  10. 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.

    Article  MathSciNet  Google Scholar 

  11. 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. L. Kleinrock, Communication Nets: Stochastic Message Flow and Delay, McGraw-Hill, New York, 1964.

    Google Scholar 

  13. L. Kleinrock, Queuing Systems, John Wiley, New York, 1976.

    Google Scholar 

  14. 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. M. Minoux, Programmation Mathématique, Dunod, Paris, 1983.

    MATH  Google Scholar 

  16. S. Nash and A. Sofer, Block truncated Newton methods for parallel optimization, Mathematical Programming, 45 (1989), pp. 529–546.

    Article  MATH  MathSciNet  Google Scholar 

  17. R. Rockafellar, Convex Analysis, Princeton University Press, Princeton, 1970.

    MATH  Google Scholar 

  18. R. Rockafellar, Network Flows and Monotropic Optimization, John Wiley & Sons, New York, 1984.

    MATH  Google Scholar 

  19. 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. T. Stern, A class of decentralized routing algorithms using relaxation, IEEE Trans. on Communications, COM 25 (1977), pp. 1092–1102.

    Article  Google Scholar 

  21. D. Young, Iterative solution of large linear systems, Academic Press, New York, 1971.

    MATH  Google Scholar 

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L. D. Davisson A. G. J. MacFarlane H. Kwakernaak J. L. Massey Ya Z. Tsypkin A. J. Viterbi Peter Kall

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© 1992 International Federation for Information Processing

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Ribeiro, C., El Baz, D. (1992). A dual method for optimal routing in packet-switched networks. In: Davisson, L.D., et al. System Modelling and Optimization. Lecture Notes in Control and Information Sciences, vol 180. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0113287

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  • DOI: https://doi.org/10.1007/BFb0113287

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-55577-3

  • Online ISBN: 978-3-540-47220-9

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