Maximal Lattice-Free Convex Sets in Linear Subspaces

References

• Andersen K., Louveaux Q., Weismantel R. Certificates of linear mixed integer infeasibility. Oper. Res. Lett. (2008) 36:734–738Crossref, Google Scholar
• Andersen K., Louveaux Q., Weismantel R. An analysis of mixed integer linear sets based on lattice point free convex sets. Math. Oper. Res. (2010) 35:233–256Link, Google Scholar
• Andersen K., Louveaux Q., Weismantel R. Mixed-integer sets associated from two rows of two adjacent simplex bases. Math. Programming B (2010) 124:455–480Crossref, Google Scholar
• Andersen K., Wagner C., Weismantel R. On an analysis of the strength of mixed integer cutting planes from multiple simplex tableau rows. SIAM J. Optim. (2009) 20:967–982Crossref, Google Scholar
• Andersen K., Louveaux Q., Weismantel R., Wolsey L. A. Cutting planes from two rows of a simplex tableau. Proc. IPCO XII (2007) 4513(June):1–15Lecture Notes in Computer ScienceGoogle Scholar
• Balas E. Intersection cuts—A new type of cutting planes for integer programming. Oper. Res. (1971) 19:19–39Link, Google Scholar
• Barvinok A., Gehring F. W., Halmos P. R., Moore C. C. A course in convexity. Graduate Studies in Mathematics (2002) 54(American Mathematical Society, Providence, Rhode Island) Google Scholar
• Basu A., Cornuéjols G., Zambelli G. Convex sets and minimal sublinear functions. J. Convex Anal. (2011) 18(2). ePub ahead of print, http://www.heldermann.de/JCA/JCA18/JCA182/jca18027.htmGoogle Scholar
• Basu A., Bonami P., Cornuéjols G., Margot F. On the relative strength of split, triangle and quadrilateral cuts. Math. Programming (2009) . ePub ahead of print April 23, http://hal.archives-ouvertes.fr/hal-00421757/en/Google Scholar
• Borozan V., Cornuéjols G. Minimal valid inequalities for integer constraints. Math. Oper. Res. (2009) 34:538–546Link, Google Scholar
• Cassels J. W. S. An introduction to the geometry of numbers. Grundlehren Mathematischen Wissenschaften (1959) 99(Springer, Berlin) Crossref, Google Scholar
• Conway J. B. A course in functional analysis. Graduate Texts in Mathematics (1990) (Springer, Berlin) Google Scholar
• Cornuéjols G., Margot F. On the facets of mixed integer programs with two integer variables and two constraints. Math. Programming Ser. A (2009) 120:429–456Crossref, Google Scholar
• Dey S. S., Wolsey L. A. Lifting integer variables in minimal inequalities corresponding to lattice-free triangles. IPCO 2008 (2008) 5035(May):463–475Lecture Notes in Computer ScienceGoogle Scholar
• Dey S. S., Wolsey L. A. Constrained infinite group relaxations of MIPs. SIAM J. Optim. (2009) March). ForthcomingGoogle Scholar
• Doignon J. P. Convexity in crystallographic lattices. J. Geometry (1973) 3:71–85Crossref, Google Scholar
• Espinoza D. Computing with multi-row Gomory cuts. Proc. IPCO XIII (2008) 5035Bertinoro, Italy:214–224Lecture Notes in Computer ScienceCrossref, Google Scholar
• Gomory R. G. Some polyhedra related to combinatorial problems. Linear Algebra Appl. (1969) 2:451–558Crossref, Google Scholar
• Gomory R. E. Thoughts about integer programming. 50th Anniversary Sympos. OR (2007) . University of Montreal, January, and Corner polyhedra and two-equation cutting planes. George Nemhauser Sympos., Atlanta, JulyGoogle Scholar
• Gomory R. E., Johnson E. L. Some continuous functions related to corner polyhedra. Math. Programming (1972) 3:23–85Crossref, Google Scholar
• Hiriart-Urruty J.-B., Lemaréchal C.Fundamentals of Convex Analysis (2001) (Springer, Berlin) Crossref, Google Scholar
• Lenstra A. H. Integer programming with a fixed number of variables. Math. Oper. Res. (1983) 8:538–548Link, Google Scholar
• Lovász L., Iri M., Tanabe K. Geometry of numbers and integer programming. Mathematical Programming: Recent Developements and Applications (1989) (Kluwer, Dordrecht, The Netherlands) 177–210Google Scholar
• Schrijver A.Theory of Linear and Integer Programming (1986) (Wiley, New York) Google Scholar
• Zambelli G. On degenerate multi-row gomory cuts. Oper. Res. Lett. (2009) 37:21–22Crossref, Google Scholar