Minimal inequalities for an infinite relaxation of integer programs

SIAM Journal on Discrete Mathematics

Volumn 24, Issue 1, 2010, Pages 158-168

  Basu, Amitabh ^a   Conforti, Michele ^b   Cornuéjols, Gérard ^c   Zambelli, Giacomo ^b  

^a CARNEGIE MELLON UNIVERSITY   (United States)

^b UNIVERSITY OF PADOVA   (Italy)

^c CARNEGIE MELLON UNIVERSITY   (United States)

Author keywords

Cutting planes; Integer programming; Maximal lattice free convex sets

Indexed keywords

GEOMETRY; SET THEORY;

CONVEX SET; CUTTING PLANES; INFINITE RELAXATION; INTEGER PROGRAM; LATTICE-FREE; RATIONAL POLYHEDRONS;

INTEGER PROGRAMMING;

EID: 77952487444     PISSN: 08954801     EISSN: None     Source Type: Journal    
DOI: 10.1137/090756375     Document Type: Article

References (11)

1. K. Andersen, Q. Louveaux, R. Weismantel, and L. A. Wolsey, Cutting Planes from Two Rows of a Simplex Tableau, in Proceedings of the IPCO XII, Ithaca, NY, Lect. Notes Comput. Sci. 4513, Springer, Berlin, 2007, pp. 1-15.
2. E. Balas, Intersection cuts-A new type of cutting planes for integer programming, Oper. Res., 19 (1971), pp. 19-39.
3. A. Barvinok, A Course in Convexity, Graduate Studies in Mathematics, Vol.54, American Mathematical Society, Providence, RI, 2002.
4. A. Basu, M. Conforti, G. Cornuéjols, and G. Zambelli, Maximal Lattice-Free Convex Sets in Linear Subspaces, manuscript, 2009.
5. A. Basu, G. Cornuéjols, and G. Zambelli, Convex Sets and Minimal Sublinear Functions, manuscript, 2009.
6. V. Borozan and G. Cornuéjols, Minimal valid inequalities for integer constraints, Math. Oper. Res., 34 (2009), pp. 538-546.
7. S. S. Dey and L. A. Wolsey, Constrained Infinite Group Relaxations of MIPs, manuscript, 2009.
8. E. L. Johnson, Characterization of facets for multiple right-hand side choice linear programs, Math. Program. Study, 14 (1981), pp. 112-142.
9. L. Lov́asz, Geometry of Numbers and Integer Programming, Mathematical Programming: Recent Developments and Applications, M. Iri and K. Tanabe eds., Kluwer, Norwell, MA, (1989), pp. 177-210.
10. A. Schrijver, Theory of Linear and Integer Programming, Wiley, New York, 1986.
11. G. Zambelli, On degenerate multi-row Gomory cuts, Oper. Res. Lett., 37 (2009), pp. 21-22.