Minimal Valid Inequalities for Integer Constraints

Published Online:https://doi.org/10.1287/moor.1080.0370

References

  • Andersen K., Louveaux Q., Weismantel R., Wolsey L. Cutting planes from two rows of a simplex tableau. Integer Programming Combinat. Optim. Conf. XII (2007) Ithaca, NY(Springer, New York) 1–15Google Scholar
  • Balas E. Intersection cuts—A new type of cutting planes for integer programming. Oper. Res. (1971) 19:19–39LinkGoogle Scholar
  • Basu A., Bonami P., Cornuéjols G., Margot F. On the relative strength of split, triangle and quadrilateral cuts. (2008) . Working Paper E-38, Tepper School of Business, Carnegie Mellon University, PittsburghGoogle Scholar
  • Basu A., Conforti M., Cornuéjols G., Zambelli G. Maximal lattice-free convex subsets of linear spaces. Math Oper. Res. (2009) . ForthcomingGoogle Scholar
  • Bell D. E. A theorem concerning the integer lattice. Stud. Appl. Math. (1977) 56:187–188CrossrefGoogle Scholar
  • Cook W., Kannan R., Schrijver A. Chvátal closures for mixed integer programming problems. Math. Programming (1990) 47:155–174CrossrefGoogle Scholar
  • Cornuéjols G., Margot F. On the facets of mixed integer programs with two integer variables and two constraints. Math. Programming (2008) . (published online May 2008), http://dx.doi.org/10.1007/s10107-008-0221-1Google Scholar
  • Dey S. S., Richard J.-P. P. Facets for the two-dimensional infinite group problems. Math. Oper. Res. (2008) 33:140–166LinkGoogle Scholar
  • Dey S. S., Wolsey L. A. Lifting integer variables in minimal inequalities corresponding to lattice-free triangles. Integer Programming Combinat. Optim. XIII (2008) Bertinoro, Italy(Springer, New York) 463–475CrossrefGoogle Scholar
  • Doignon J.-P. Convexity in cristallographical lattices. J. Geometry (1973) 3:71–85CrossrefGoogle Scholar
  • Espinoza D. Computing with multi-row Gomory cuts. Integer Programming Combinat. Optim. XIII (2008) Bertinoro, Italy(Springer, New York) 214–224CrossrefGoogle Scholar
  • Gomory R. E., Graves R. L., Wolfe P. An algorithm for integer solutions to linear programs. Recent Advances in Mathematical Programming (1963) (McGraw-Hill, New York) 269–302Google Scholar
  • Gomory R. G. Some polyhedra related to combinatorial problems. Linear Algebra Appl. (1969) 2:451–558CrossrefGoogle Scholar
  • Gomory R. E. Thoughts about integer programming. (2007) . 50th Anniversary Sympos. OR, University of Montreal, Quebec, and Corner polyhedra and two-equation cutting planes. George Nemhauser Sympos., AtlantaGoogle Scholar
  • Gomory R. E., Johnson E. L. Some continuous functions related to corner polyhedra, Part I. Math. Programming (1972) 3:23–85CrossrefGoogle Scholar
  • Lovász L., Iri M., Tanabe K. Geometry of numbers and integer programming. Mathematical Programming: Recent Developments and Applications (1989) (Kluwer Academic Publishers, Dordrecht, The Netherlands) 177–201Google Scholar
  • Marchand H., Wolsey L. A. Aggregation and mixed integer rounding to solve MIPs. Oper. Res. (2001) 49:363–371LinkGoogle Scholar
  • Nemhauser G. L., Wolsey L. A.Integer and Combinatorial Optimization (1988) (John Wiley and Sons, New York) CrossrefGoogle Scholar
  • Scarf H. E. An observation on the structure of production sets with indivisibilities. Proc. National Acad. Sci. (1977) 74:3637–3641CrossrefGoogle Scholar
  • Zambelli G. On degenerate multi-row Gomory cuts. Oper. Res. Lett. (2009) 37(1):21–22CrossrefGoogle 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.