User menu

Two row mixed-integer cuts via lifting

Bibliographic reference Dey, Santanu S. ; Wolsey, Laurence. Two row mixed-integer cuts via lifting. In: Mathematical Programming, Vol. 124, no. 1-2, p. 143-174 (Juillet 2010)
Permanent URL http://hdl.handle.net/2078.1/33407
  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.) Proceedings 12th Conference on Integer Programming and Combinatorial Optimization, pp. 1–15. Springer (2007)
  2. Aráoz J., Evans L., Gomory R.E., Johnson E.L.: Cyclic group and knapsack facets. Math. Prog. 96, 377–408 (2003)
  3. Balas E.: Disjunctive programming. Ann. Discrete Math. 5, 3–51 (1979)
  4. Balas E.: Intersection cuts—a new type of cutting planes for integer programming. Oper. Res. 19, 19–39 (1971)
  5. Balas E., Jeroslow R.: Strengthening cuts for mixed integer programs. Eur. J. Oper. Res. 4, 224–234 (1980)
  6. Borozan, V., Cornuéjols, G.: Minimal valid inequalities for integer constraints. http://integer.tepper.cmu.edu (2007)
  7. Cook W.J., Kannan R., Schrijver A.: Chvátal closures for mixed integer programming problems. Math. Prog. 47, 155–174 (1990)
  8. Cornuéjols G., Li Y.: Elementary closures for integer programs. Oper. Res. Lett. 28, 1–8 (2001)
  9. Cornuéjols, G., Margot, F.: On the facets of mixed integer programs with two integer variables and two constraints. To appear in Math. Prog. (2008)
  10. Cornuéjols G., Li Y., Vandenbussche D.: K-cuts: a variation of Gomory mixed integer cuts from the LP tableau. INFORMS J. Comput. 15, 385–396 (2003)
  11. Dash S., Günlük O.: Valid inequalities based on simple mixed-integer sets. Math. Prog. 105, 29–53 (2006)
  12. Dash, S., Günlük, O.: On the strength of Gomory mixed-integer cuts as group cuts. Technical Report RC23967, IBM Research report (2006b)
  13. Dey, S.S., Richard, J.-P.P.: Sequential-merge facets for two-dimensional group problems. In: Fischetti, M., Williamson, D.P. (eds.) Proceedings 12th Conference on Integer Programming and Combinatorial Optimization, pp. 30–42. Springer (2007)
  14. Dey S.S., Richard J.-P.P.: Facets of two-dimensional infinite group problems. Math. Oper. Res. 33, 140–166 (2008)
  15. Dey, S.S., Wolsey, L.A.: Lifting integer variables in minimal inequalities corresponding to lattice-free triangles. In: Lodi, A., Panconesci, A., Rinaldi, G. (eds.) Proceedings 13th Conference on Integer Programming and Combinatorial Optimization, pp. 463–475. Springer (2007)
  16. Dey, S.S., Wolsey, L.A.: Two row mixed integer cuts via lifting. Technical Report 30, CORE DP, Université catholique de Louvain, Louvain-la-Neuve, Belgium (2008)
  17. Fischetti M., Saturni C.: Mixed integer cuts from cyclic groups. Math. Prog. 109, 27–53 (2007)
  18. Gomory R.E.: Some polyhedra related to combinatorial problems. Linear Algebra Appl. 2, 451–558 (1969)
  19. Gomory, R.E.: An algorithm for the mixed-integer problem. Technical Report RM-2597, Rand Report (1960)
  20. Gomory R.E., Johnson E.L.: Some continuous functions related to corner polyhedra, part I. Math. Prog. 3, 23–85 (1972)
  21. Gomory R.E., Johnson E.L.: Some continuous functions related to corner polyhedra, part II. Math. Prog. 3, 359–389 (1972)
  22. Gomory R.E., Johnson E.L.: T-space and cutting planes. Math. Prog. 96, 341–375 (2003)
  23. Gomory R.E., Johnson E.L., Evans L.: Corner polyhedra and their connection with cutting planes. Math. Prog. 96, 321–339 (2003)
  24. Johnson Ellis L., On the group problem for mixed integer programming, Approaches to Integer Programming (1974) ISBN:9783642007392 p.137-179, 10.1007/bfb0120692
  25. Johnson Ellis L., Characterization of facets for multiple right-hand choice linear programs, Mathematical Programming Studies (1981) ISBN:9783642008054 p.112-142, 10.1007/bfb0120925
  26. Lovász L.: Geometry of numbers and integer programming. In: Iri, M., Tanabe, K. (eds) Mathematical Programming: Recent Developments and Applications, Kluwer, Dordrecht (1989)
  27. Miller L.A., Li Y., Richard J.-P.P.: New facets for finite and infinite group problems from approximate lifting. Naval Res. Logis. 55, 172–191 (2008)
  28. Nemhauser G.L., Wolsey L.A.: A recursive procedure to generate all cuts for 0–1 mixed integer programs. Math. Prog. 46, 379–390 (1990)
  29. Nemhauser George, Wolsey Laurence, Integer and Combinatorial Optimization : Nemhauser/Integer and Combinatorial Optimization, ISBN:9781118627372, 10.1002/9781118627372
  30. Richard, J.-P.P., Li, Y., Miller, L.A.: Valid inequalities for MIPs and group polyhedra from approximate liftings. Math. Prog. 118, 253–277 (2009)
  31. Rockafellar Ralph Tyrell, Convex Analysis : , ISBN:9781400873173, 10.1515/9781400873173