On lifting integer variables in minimal inequalities

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 6080 LNCS, Issue , 2010, Pages 85-95

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

^a CARNEGIE MELLON UNIVERSITY   (United States)

^b FEDERAL UNIVERSITY OF CEARÁ   (Brazil)

^c UNIVERSITY OF PADOVA   (Italy)

^d AIX MARSEILLE UNIV   (France)

Author keywords

[No Author keywords available]

Indexed keywords

CONTINUOUS VARIABLES; CONVEX POLYHEDRONS; CUTTING PLANES; INTEGER VARIABLES; LIFTING FUNCTIONS; MIXED INTEGER LINEAR PROGRAM; NONCONVEX; VALID INEQUALITY;

COMBINATORIAL OPTIMIZATION; DYNAMIC PROGRAMMING;

INTEGER PROGRAMMING;

EID: 77954420918     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/978-3-642-13036-6_7     Document Type: Conference Paper

References (15)

1. Andersen, K., Louveaux, Q., Weismantel, R., Wolsey, L.A.: Cutting Planes from Two Rows of a Simplex Tableau. In: Fischetti, M., Williamson, D.P. (eds.) IPCO 2007. LNCS, vol. 4513, pp. 1-15. Springer, Heidelberg (2007)
2. Balas, E.: Intersection Cuts - A New Type of Cutting Planes for Integer Programming. Operations Research 19, 19-39 (1971)
3. Barvinok, A.: A Course in Convexity. In: Graduate Studies in Mathematics, vol. 54. American Mathematical Society, Providence (2002)
4. Basu, A., Conforti, M., Cornuejols, G., Zambelli, G.: A Counterexample to a Conjecture of Gomory and Johnson. Mathematical Programming Ser. A (to appear 2010)
5. Basu, A., Conforti, M., Cornuejols, G., Zambelli, G.: Maximal Lattice-free Convex Sets in Linear Subspaces (2009) (manuscript)
6. Basu, A., Conforti, M., Cornuejols, G., Zambelli, G.: Minimal Inequalities for an Infinite Relaxation of Integer Programs. SIAM Journal of Discrete Mathematics (to appear 2010)
7. Borozan, V., Cornuéjols, G.: Minimal Valid Inequalities for Integer Constraints. Mathematics of Operations Research 34, 538-546 (2009)
8. Conforti, M., Cornuejols, G., Zambelli, G.: A Geometric Perspective on Lifting (May 2009) (manuscript)
9. Dey, S.S., Wolsey, L.A.: Lifting Integer Variables in Minimal Inequalities corresponding to Lattice-Free Triangles. In: Lodi, A., Panconesi, A., Rinaldi, G. (eds.) IPCO 2008. LNCS, vol. 5035, pp. 463-475. Springer, Heidelberg (2008)
10. Dey, S.S., Wolsey, L.A.: Constrained Infinite Group Relaxations of MIPs (March 2009) (manuscript)
11. Gomory, R.E.: Some Polyhedra related to Combinatorial Problems. Linear Algebra and its Applications 2, 451-558 (1969)
12. Gomory, R.E., Johnson, E.L.: Some Continuous Functions Related to Corner Polyhedra, Part I. Mathematical Programming 3, 23-85 (1972)
13. Johnson, E.L.: On the Group Problem for Mixed Integer Programming. In: Mathematical Programming Study, pp. 137-179 (1974)
14. Schrijver, A.: Theory of Linear and Integer Programming. John Wiley & Sons, New York (1986)
15. Meyer, R.R.: On the Existence of Optimal Solutions to Integer and Mixed-Integer Programming Problems. Mathematical Programming 7, 223-235 (1974)