Composite lifting of group inequalities and an application to two-row mixing inequalities

Discrete Optimization

Volumn 7, Issue 4, 2010, Pages 256-268

  Dey, Santanu S ^a   Wolsey, Laurence A ^b  

^a GEORGIA INSTITUTE OF TECHNOLOGY   (United States)

^b UNIVERSITÉ CATHOLIQUE DE LOUVAIN   (Belgium)

Author keywords

Infinite group relaxations; Mixed integer programs; Mixing inequalities

Indexed keywords

INFINITE GROUPS; MIXED INTEGER; MIXED-INTEGER PROGRAMS; VALID INEQUALITY;

MIXING;

INTEGER PROGRAMMING;

EID: 77955519126     PISSN: 15725286     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.disopt.2010.06.001     Document Type: Article

References (17)

1. R.E. Gomory, and E.L. Johnson Some continuous functions related to corner polyhedra, part I Mathematical Programming 3 1972 23 85
2. R.E. Gomory, and E.L. Johnson Some continuous functions related to corner polyhedra, part II Mathematical Programming 3 1972 359 389
3. E.L. Johnson On the group problem for mixed integer programming Mathematical Programming Study 2 1974 137 179
4. K. Andersen, Q. Louveaux, R. Weismantel, and L. Wolsey Cutting planes from two rows of a simplex tableau M. Fischetti, D.P. Williamson, Integer Programming and Combinatorial Optimization, 12th International IPCO Conference, Ithaca, NY, USA, June 2527, 2007, Proceedings Lecture Notes in Computer Science vol. 4513 2007 Springer 1 15
5. A. Basu, M. Conforti, G. Cornujols, and G. Zambelli Minimal inequalities for an infinite relaxation of integer programs SIAM Journal on Discrete Mathematics 24 2010 158 168
6. G. Cornujols, and F. Margot On the facets of mixed integer programs with two integer variables and two constraints Mathematical Programming 120 2009 429 456
7. G. Zambelli On degenerate multi-row Gomory cuts Operations Research Letters 37 2009 21 22
8. S.S. Dey, L.A. Wolsey, Two row mixed integer cuts via lifting, Mathematical Programming B (2010), doi:10.1007/s10107-010-0362-x.
9. M. Conforti, G. Cornujols, G. Zambelli, A geometric perspective on lifting, 2009. http://www.math.unipd.it/~giacomo/.
10. A. Basu, M. Campelo, M. Conforti, G. Cornujols, and G. Zambelli On lifting integer variables in minimal inequalities F. Eisenbrand, F.B. Shepherd, Integer Programming and Combinatorial Optimization, 14th International Conference, IPCO 2010, Lausanne, Switzerland, June 911, 2010, Proceedings Lecture Notes in Computer Science vol. 6080 2010 Springer 85 95
11. E. Balas, and R. Jeroslow Strenghtening cuts for mixed integer programs European Journal of Operations Research 4 1980 224 234
12. S.S. Dey, J.-P.P. Richard, Y. Li, and L.A. Miller Extreme inequalities for infinite group problems Mathematical Programming 121 2010 145 170
13. S.S. Dey, and J.-P.P. Richard Facets of two-dimensional infinite group problems Mathematics of Operations Research 33 2008 140 166
14. O. Gnlk, and Y. Pochet Mixing mixed-integer inequalities Mathematical Programming 90 2001 429 457
15. S.S. Dey, A note on the split rank of intersection cuts, Mathematical Programming (2010), doi:10.1007/s10107-009-0329-y.
16. S.S. Dey, and L.A. Wolsey Lifting integer variables in minimal inequalities corresponding to lattice-free triangles A. Lodi, A. Panconesi, G. Rinaldi, Integer Programming and Combinatorial Optimization, 13th International Conference, IPCO 2008, Bertinoro, Italy, May 2628, 2008, Proceedings Lecture Notes in Computer Science vol. 5035 2008 Springer 463 475
17. S. Dash, and O. Gnlk On mixing inequalities: rank, closure and cutting plane proofs SIAM Journal on Optimization 2010 1090 1109