no. 4
Résolution de programmes linéaires entiers ou mixtes à l'aide de la forme normale de Hermite
RAIRO - Operations Research - Recherche Opérationnelle, Tome 31 (1997) no. 4, pp. 399-427 
@article{RO_1997__31_4_399_0,
     author = {Maublanc, J. and Quilliot, A.},
     title = {R\'esolution de programmes lin\'eaires entiers ou mixtes \`a l'aide de la forme normale de {Hermite}},
     journal = {RAIRO - Operations Research - Recherche Op\'erationnelle},
     pages = {399--427},
     year = {1997},
     publisher = {EDP Sciences},
     volume = {31},
     number = {4},
     mrnumber = {1491046},
     zbl = {0888.90124},
     language = {fr},
     url = {https://www.numdam.org/item/RO_1997__31_4_399_0/}
}
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Maublanc, J.; Quilliot, A. Résolution de programmes linéaires entiers ou mixtes à l'aide de la forme normale de Hermite. RAIRO - Operations Research - Recherche Opérationnelle, Tome 31 (1997) no. 4, pp. 399-427. https://www.numdam.org/item/RO_1997__31_4_399_0/

1. E. B. Balas, Intersection n-cuts-a new type of cutting planes for integer programming, Operat. Research, 1971, 19, p. 19-39. | Zbl

2. F. L. Bauer, Algorithms 153 Gomory; Comunications of the ACM, 1963, 6, p. 68.

3. R. Bixby et W. Cunningham, Converting linear programs to network problems; Maths of Operat. Research, 1980, 5, p. 321-357. | Zbl | MR

4. V. J. Bowman et G. L. Nemhauser, A finiteness proof for modified Dantzig cuts in integer programming: Naval Research Log Quarter, 1970, 17, p. 309-313. | Zbl | MR

5. V. J. Bowman et G. L. Nemhauser, Deep cuts in integer programming; Operat Research, 1971, 8, p. 89-111. | MR

6. M. Carter, A survey on practical applications of examination timetabling algorithms; Operat Research, 1986, 34, 2, p. 193-302. | MR

7. A. Charnes et W. Cooper, Management models and industrial applications of linear programming, J. WILEY and sons, 1961. | Zbl | MR

8. V. Chvatal, Cutting planes and combinatorics; European Journal of combinatorics, 1985, 6, p. 217-226. | Zbl | MR

9. R. J. Dakin, A tree search algorithm for mixed integer programming problems, The Computer Journal, 1965, 8, p. 250-255. | Zbl | MR

10. P. D. Damich, R. Kannan et L. Trotter, Hermite normal form computation using modulo determinant arithmetic: Math. Operat. Research, 1987, 12, 1, p. 50-59. | Zbl | MR

11. J. Edmonds, F. Giles, Total dual integrality of linear inequality Systems in Progress in Combinatorial Optimization, Acad. Press. Toronto, 1984, p. 117-129. | Zbl | MR

12. D. Fayard et G. Plateau, An efficient algorithm for the 0-1 knapsack problem, R. M. NAUSS, Management Sciences, 1977, 24, p. 918-919.

13. M. Garey et D. Johnsson, Computer and intractability; W. FREEMAN and Co. N.Y., 1979. | Zbl

14. R. Garfinkel et G. L. Nemhauser, Integer programming; J. WILEY and sons, N.Y., 1972. | Zbl | MR

15. A. M. Geoffrion, Lagrangean relaxation for integer programming; Math Programming Study 2, 1974, p. 82-114. | Zbl | MR

16. F. Glover, Generalized cuts in Diophantine programming, Management Sciences 13, 1966-1967, p. 254-268. | Zbl | MR

17. S. Godano, Méthodes géométriques pour la programmation linéaire, Thèse Université Blaise Pascal, Clermont-Ferrand, 1994.

18. R. E. Gomory, Outlines of an algorithm for integer solutions to linear programs, Bull American Math. Soc., 1958, 64, p. 275-278. | Zbl | MR

19. R. E. Gomory, An algorithm for integer solutions to linear programs, Recent Advances in Math. programming. (R. L. GRAVES and P. WOLFE Eds.), Mac Graw Hill, N.Y., 1963, p. 269-302. | Zbl | MR

20. M. Gondran, Un outil pour la programmation en nombres entiers, la méthode des congruences décroissantes : RAIRO 3, 1973, p. 35-54. | Zbl | MR | Numdam

21. M. Grotschel, L. Lovacz et A. Schrijver, The ellipsoid method and combinatorial optimization, Springer-Verlag, Heidelberg, 1986.

22. M. Held et R. Karp, The travelling salesman problem and minimum spanning trees, Operat. Research 18, 1970, p. 1138-1162. | Zbl | MR

23. A. Hoffman et J. Kruskal, Integral boundary points of integer polyedra in Linear Inequalities and Related Systems, H. KUHN and A. TUCKER Eds., Princeton Univ. Press, 1986, p. 223-246. | Zbl

24. R. Kannan et A. Bachem, Polynomial algorithms for Computing the Smith and Hermite normal forms of an integer matrix; SIAM Journ. Comput 8, 1979, 4, p. 499-507. | Zbl

25. H. Langmaack, Algorithm 263 Gomory 1 [H]; Communications of the ACM, 1965, 8, p. 601-602.

26. H. Lenstra, Integer Programming with a flxed number of variables, Maths of Operat. Research, 1983, 8, p. 538-548. | Zbl

27. L. G. Proll, Certification of algorithm 263A [H] Gomory 1, Comm. ACM 13, 1970, p. 326-327.

28. I. Rosemberg, On Chvatal's cutting planes in integer programming, Mathematische Operation Forschung und Statistik, 1975, 6, p. 511-522. | Zbl | MR

29. A. Schrijver, Theory of linear and integer programming, Wiley, Chichester, 1986. | Zbl | MR

30 A. V. Srinivasan, An investigation of some computational aspects of integer programming, JACM 12, 1965, p. 525-535. | Zbl