On the Rank of Disjunctive Cuts

Published Online:https://doi.org/10.1287/moor.1110.0527

References

  • Andersen K., Cornuéjols G., Li Y. Split closure and intersection cuts. Math. Programming (2005) 102(3):457–493CrossrefGoogle Scholar
  • Balas E. Intersection cuts—A new type of cutting planes for integer programming. Oper. Res. (1971) 19(1):19–39LinkGoogle Scholar
  • Balas E. Disjunctive programming: Properties of the convex hull of feasible points. Discrete Appl. Math. (1998) 89(1–3):3–44CrossrefGoogle Scholar
  • Balas E., Saxena A. Optimizing over the split closure. Math. Programming (2008) 113(2):219–240CrossrefGoogle Scholar
  • Basu A., Cornuéjols G., Margot F. Intersection cuts with infinite split rank. Math. Oper. Res. (2012) 37(1):21–40LinkGoogle Scholar
  • Cook W. J., Kannan R., Schrijver A. Chvátal closures for mixed integer programming problems. Math. Programming (1990) 47(1–3):155–174CrossrefGoogle Scholar
  • Del Pia A., Weismantel R. On convergence in mixed integer programming. Math. Programming (2012) . ForthcomingGoogle Scholar
  • Dey S. S., Louveaux Q. Split rank of triangle and quadrilateral inequalities. Math. Oper. Res. (2011) 36(3):432–461LinkGoogle Scholar
  • Gomory R. E. Outline of an algorithm for integer solutions to linear programs. Bull. Amer. Math. Soc. (1958) 64(5):275–278CrossrefGoogle Scholar
  • Jörg M. k-disjunctive cuts and cutting plane algorithms for general mixed integer linear programs. (2008) . Ph.D. thesis, Technische Universität München, München, GermanyGoogle Scholar
  • Lovász L., Iri M., Tanabe K. Geometry of numbers and integer programming. Mathematical Programming: Recent Developments and Applications (1989) (Kluwer Academic, Dordrecht, The Netherlands) 177–201Google Scholar
  • Meyer R. R. On the existence of optimal solutions to integer and mixed-integer programming problems. Math. Programming (1974) 7(1):223–235CrossrefGoogle Scholar
  • Owen J. H., Mehrotra S. A disjunctive cutting plane procedure for general mixed integer linear programs. Math. Programming (2001) 89(3):437–448CrossrefGoogle Scholar
  • Rockafellar R. T.Convex Analysis (1970) (Princeton University Press, Princeton, NJ) CrossrefGoogle Scholar
  • Salinetti G., Wets R. J.-B. On the convergence of sequences of convex sets in finite dimensions. Soc. Indust. Appl. Math. (1979) 21(1):18–33Google Scholar
  • Schrijver A.Theory of Linear and Integer Programming (1986) (Wiley, Chichester, UK) Google Scholar
INFORMS site uses cookies to store information on your computer. Some are essential to make our site work; Others help us improve the user experience. By using this site, you consent to the placement of these cookies. Please read our Privacy Statement to learn more.