Le traitement des solutions quasi optimales en programmation linéaire continue : une synthèse

J. Siskos

RAIRO - Operations Research - Recherche Opérationnelle (1984)

  • Volume: 18, Issue: 4, page 381-401
  • ISSN: 0399-0559

How to cite

top

Siskos, J.. "Le traitement des solutions quasi optimales en programmation linéaire continue : une synthèse." RAIRO - Operations Research - Recherche Opérationnelle 18.4 (1984): 381-401. <http://eudml.org/doc/104862>.

@article{Siskos1984,
author = {Siskos, J.},
journal = {RAIRO - Operations Research - Recherche Opérationnelle},
keywords = {continuous linear programming; survey; optimal solutions; near-optimal solutions; quasi-optimal solutions; degenerate linear programming; inverse simplex method; labyrinth method; heuristic methods},
language = {fre},
number = {4},
pages = {381-401},
publisher = {EDP-Sciences},
title = {Le traitement des solutions quasi optimales en programmation linéaire continue : une synthèse},
url = {http://eudml.org/doc/104862},
volume = {18},
year = {1984},
}

TY - JOUR
AU - Siskos, J.
TI - Le traitement des solutions quasi optimales en programmation linéaire continue : une synthèse
JO - RAIRO - Operations Research - Recherche Opérationnelle
PY - 1984
PB - EDP-Sciences
VL - 18
IS - 4
SP - 381
EP - 401
LA - fre
KW - continuous linear programming; survey; optimal solutions; near-optimal solutions; quasi-optimal solutions; degenerate linear programming; inverse simplex method; labyrinth method; heuristic methods
UR - http://eudml.org/doc/104862
ER -

References

top
  1. 1. M. L. BALINSKI, An Algorithm for Finding all Vertices of Convex Polyhedral Sets, J. Soc. Indust. Appl. Math., vol. 9, n° 1, 1961, p. 72-88. Zbl0108.33203MR142057
  2. 2. A. CHARNES, Optimality and Degeneracy in Linear Programming, Econometrika, vol. 20, 1952, p. 160-170. Zbl0049.37903MR56264
  3. 3. A. CHARNES et W. W. COOPER, Management Models and Industrial Applications of Linear Programming, John Wiley and Sons, vol. 1, New York, 1961. Zbl0107.37004MR157773
  4. 4. N. V. CHERNIKOVA, Algorithm for Finding a General Formula for the Non-Negative Solutions of a System of Linear Inequalities, U.S.S.R. Computational Mathematics and Mathematical Physics, vol. V, 1965, p. 228-233. Zbl0171.35701
  5. 5. M. E. DYER et L. G. PROLL, Vertex Enumeration in Convex Polyhedra: A Comparative Computational Study, in T. B. BOFFEY, éd., Proc. CP77 Combinatorial Programming Conference, University of Liverpool, Liverpool, 1977, p. 23-43. 
  6. 6. M. E. DYER et L. G. PROLL, An Improved Vertex Enumeration Algorithm, European Journal of Operational Research, vol. 9, 1982, p. 359-368. Zbl0477.90035MR655093
  7. 7. R. FAURE, La programmation linéaire appliquée, Que sais-je ?, n° 1776, P.U.F., Paris, 1979. 
  8. 8. R. FAURE, Précis de recherche opérationnelle (4e éd. entièrement refondue d'Éléments de la Recherche Opérationnelle, 1968), Dunod, Paris, 1979. 
  9. 9. T. GAL et J. NEDOMA, Multiparametric Linear Programming, Management Science, vol. 18, 1972, p. 406-422. Zbl0237.90037MR292502
  10. 10. T. GAL, Postoptimal Analyses, Parametric Programming, and Related Topics, MacGraw Hill, New York, 1979. Zbl0407.90052MR536349
  11. 11. H. GREENBERG, An Algorithm for Determining Redundant Inequalities and all Solutions to Convex Polyhedra, Numerische Mathematik, vol. 24, 1975, p. 19-26. Zbl0288.65041MR426423
  12. 12. G. HADLEY, Linear Programming, Addison-Wesley, Reading, Massachusetts, 1962. Zbl0102.36304MR135622
  13. 13. J. P. IGNIZIO, Goal Programming and Extensions, Lexington Books, D.C. Heath and Company, Massachusetts, 1976. 
  14. 14. V. KLEE, On the Number of Vertices of a Convex Polytope, Canadian Journal of Mathematics, vol. 16, 1964, p. 701-720. Zbl0128.17201MR166682
  15. 15. M. MANAS et J. NEDOMA, Finding all Vertices of a Convex Polyhedron, Numerische Mathematik, vol. 14, 1968, p. 226-229. Zbl0165.51801MR235705
  16. 16. T. H. MATTHEISS, An Algorithm for Determining Irrelevant Constraints and all Vertices in Systems of Linear Inequalities, Operations Research, vol. 21, 1973, p. 247-260. Zbl0265.90024MR437087
  17. 17. T. H. MATTHEISS et D. S. RUBIN, A Survey and Comparison of Methods for Finding all Vertices of Convex Polyhedral Sets, Mathematics of Operations Research, vol. 5, 1980, p. 167-185. Zbl0442.90050MR571811
  18. 18. T. S. MOTZKIN, H. RAIFFA, G. L. THOMPSON et R. M. THRALL, The Double Description Method, in: H. W. KUHN et A. W. TUCKER, éds., Contributions to the Theory of Games, vol. 2, Princeton University Press, Princeton, New Jersey, 1953. Zbl0050.14201MR60202
  19. 19. A. OMAR, Finding all Extreme Points and Extreme Rays of a Convex Polyhedral Set, Ekonomicko-Matematicky, Obzor, vol. 3, 1977, p. 331-342. Zbl0372.90077MR470864
  20. 20. M. RIZZI, Une nouvelle méthode d'aide à la décision en avenir incertain, R.A.I.R.O. Recherche Opérationnelle, vol. 16, n° 4, 1982, p. 391-405. Zbl0506.90043
  21. 21. P. ROSENSTIEHL, Labyrinthologie mathématique, Mathématiques et Sciences Humaines, 9e année, n° 33, 1971, p. 5-32. Zbl0228.05127MR316278
  22. 22. J. SISKOS, Comment modéliser les préférences au moyen de fonctions d'utilité additives, R.A.I.R.O. Recherche Opérationnelle, vol. 14, n° 1, 1980, p. 53-82. Zbl0436.90005
  23. 23. J. SISKOS, Application de la méthode UTAI à un problème de sélection de points de vente mettant en jeu des critères multiples, R.A.I.R.O. Recherche Opérationnelle, vol. 17, n° 2, 1983, p. 121-136. 
  24. 24. G. TARRY, Le problème des labyrinthes, Nouvelles Annales de Mathématiques, vol. XIV, 1895, p. 187-190. Zbl26.0257.02JFM26.0645.02
  25. 25. C. VAN DE PANNE, Methods for Linear and Quadratic Programming, North-Holland Publishing Company, Amsterdam, 1975. Zbl0348.90094MR439021
  26. 26. H. M. WINKELS, A Flexible Decision Aid Method for Linear Multicriteria Systems, in: M. GRAUER, A. LEWANDOWSKI et A. P. WIERZBICKI, éds., Multiobjective and Stochastic Optimization, I.I.A.S.A. Collaborative Proceedings Series CP-82-812, Laxenburg (Austria), 1982, p. 377-410. 
  27. 27. H. M. WINKELS et R. COLMAN, Visualization of 5 Dimensional Polyhedra, Working paper on economathematics n° 8209, Ruhr-Universität Bochum, 1982. 
  28. 28. M. ZELENY, Linear Multiobjective Programming, Springer-Verlag, Berlin, 1974. Zbl0325.90033MR351440

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.