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},
     publisher = {EDP-Sciences},
     volume = {31},
     number = {4},
     year = {1997},
     mrnumber = {1491046},
     zbl = {0888.90124},
     language = {fr},
     url = {http://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. http://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. | MR | Zbl

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. | MR | Zbl

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. | MR | Zbl

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

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

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. | MR | Zbl

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

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. | MR | Zbl

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

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

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. | MR | Zbl

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. | MR | Zbl

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

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. | MR | Zbl

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. | MR | Zbl

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

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