Subgradient optimization and large scale programming : an application to optimum multicommodity network synthesis with security constraints

M. Minoux; J. Y. Serreault

RAIRO - Operations Research - Recherche Opérationnelle (1981)

  • Volume: 15, Issue: 2, page 185-203
  • ISSN: 0399-0559

How to cite

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Minoux, M., and Serreault, J. Y.. "Subgradient optimization and large scale programming : an application to optimum multicommodity network synthesis with security constraints." RAIRO - Operations Research - Recherche Opérationnelle 15.2 (1981): 185-203. <http://eudml.org/doc/104785>.

@article{Minoux1981,
author = {Minoux, M., Serreault, J. Y.},
journal = {RAIRO - Operations Research - Recherche Opérationnelle},
keywords = {subgradient optimization; optimum multicommodity network synthesis; security constraints; connected graph; telecommunication network optimization; Lagrangean relaxation; subgradient algorithms; computational results; Benders decomposition},
language = {eng},
number = {2},
pages = {185-203},
publisher = {EDP-Sciences},
title = {Subgradient optimization and large scale programming : an application to optimum multicommodity network synthesis with security constraints},
url = {http://eudml.org/doc/104785},
volume = {15},
year = {1981},
}

TY - JOUR
AU - Minoux, M.
AU - Serreault, J. Y.
TI - Subgradient optimization and large scale programming : an application to optimum multicommodity network synthesis with security constraints
JO - RAIRO - Operations Research - Recherche Opérationnelle
PY - 1981
PB - EDP-Sciences
VL - 15
IS - 2
SP - 185
EP - 203
LA - eng
KW - subgradient optimization; optimum multicommodity network synthesis; security constraints; connected graph; telecommunication network optimization; Lagrangean relaxation; subgradient algorithms; computational results; Benders decomposition
UR - http://eudml.org/doc/104785
ER -

References

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  1. 1. M. GONDRAN and M. MINOUX, Graphes et algorithmes, Eyrolles, Paris, 1979. Zbl0497.05023MR615739
  2. 2. M. MINOUX, Optimum Synthesis of a Network with Non Simultaneous Multicommodity Flow Requirements, Proceedings of the workshop "Application of Graph Theory and Combinatorics to management ", Brussels, March 20-21, 1979. Zbl0469.90080
  3. 3. M. MINOUX, La synthèse des réseaux de télécommunication avec contraintes de sécurité : une approche théorique, Note technique JTD/CES 68 du Centre national d'Études des Télécommunications (non publiée), 1972. 
  4. 4. M. HELD and R. M. KARP, The Travelling Salesman Problem and Minimum Spanning Trees: part II, Mathematical Programming, Vol. 1, 1971, pp. 6-25. Zbl0232.90038MR289119
  5. 5. M. HELD, P. WOLFE and H. P. CROWDER, Validation of Subgradient Optimization, Mathematical Programming, Vol. 6, No. 1, 1974, pp. 62-88. Zbl0284.90057MR341863
  6. 6. M. MINOUX, Planification à court et à moyen terme d'un réseau de télécommunications, Annales des Télécommunications, T. 29, No. 11-12, 1974, pp. 509-536. MR376132
  7. 7. M. MINOUX and J. Y. SERREAULT, Le programme d'admissibilité avec contraintes de sécurité et coûts de mutations, Annales des Télécommunications 1980 (à paraître). Zbl0423.90016
  8. 8. M. MINOUX and J. Y. SERREAULT, Synthèse optimale d'un réseau de télécommunications avec contraintes de sécurité, Annales des Télécommunications 1981 (à paraître). 
  9. 9. J. Y. SERREAULT, Calcul automatique des plans de secours dans le réseau interurbain français : présentation du programme ORSEC, Note technique du Centre national d'Études des Télécommunications, 1979 (non publié). 
  10. 10. M. MINOUXProgrammation mathématique, Cours de l'École nationale supérieure de Techniques avancées , Paris, 1978. Zbl0546.90056MR2571910
  11. 11. J. L. GOFFIN, On Convergence Rates of Subgradient Optimization Methods, Mathematical Programming, Vol. 13, 1977, pp. 329-347. Zbl0368.90119MR519665
  12. 12. S. AGMON, The Relaxation Method for Linear Inequalities, Can. J. Math., Vol. 6, 1954, pp. 382-392 Zbl0055.35001MR62786
  13. 13. T. MOTZKIN and I. J. SCHOENBERG, The Relaxation Method for Linear Inequalities, Can. J. Math., Vol. 6, 1954, pp. 393-404 Zbl0055.35002MR62787
  14. 14. N. Z. SHOR, On the Rate of Convergence of the Generalized Gradient Method, Kibernetika, Vol. 4, No. 3, 1968. Zbl0229.90044
  15. 15. J. F. BENDERS, Partitioning Procedures for Solving Mixed Variables Programming Problems, Numerische Mathematik, 4, 1962, pp. 238-252. Zbl0109.38302MR147303
  16. 16. M. MINOUX, Résolution des problèmes de multiflots en nombres entiers dans les grands réseaux, R.A.I.R.O. (France), Vol. 3, 1975, pp. 21-40. Zbl0317.90056MR421642
  17. 17. L. S. LASDON, Optimization Theory for Large Systems, Macmillan series for operations research, 1970. Zbl0224.90038MR337317
  18. 18. J. P. LEGENDRE and M. MINOUX, Une application de la notion de dualité en programmation discrète : sélection et affectation optimales d'une flotte d'avions, R.AI.R.O., Vol. 11, No. 2, 1977, pp. 201-222. Zbl0362.90038MR489867
  19. 19. J. L. KENNINGTON and M. SHALABY, An Effective Subgradient Procedure for Minimal Cost Multicommodity Flow Problems, Manag. Sc., Vol. 23, No. 9, 1977, pp. 994-1004. Zbl0366.90118

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