Approximating the Split Closure

References

• Achterberg T (2007) Constraint integer programming. Ph.D. thesis, Technische Universität Berlin, Berlin, Germany.Google Scholar
• Achterberg T, Koch T, Martin A (2006) MIPLIB 2003. Oper. Res. Lett. 34(4):1–12.Crossref, Google Scholar
• Andersen K, Weismantel R (2010) Zero-coefficient cuts. Eisenbrand F, Shepherd F, eds. Integer Programming and Combinatorial Optimization, Lecture Notes in Computer Science, Vol. 6080 (Springer, Berlin/Heidelberg), 57–70.Crossref, Google Scholar
• Andersen K, Cornuéjols G, Li Y (2005a) Reduce-and-split cuts: Improving the performance of mixed-integer gomory cuts. Management Sci. 51(11):1720–1732.Link, Google Scholar
• Andersen K, Cornuéjols G, Li Y (2005b) Split closure and intersection cuts. Math. Programming 102(3):457–493.Crossref, Google Scholar
• Andreello G, Caprara A, Fischetti M (2007) Embedding {0, 1/2}-cuts in a branch-and-cut framework: A computational study. INFORMS J. Comput. 19(2):229–238.Link, Google Scholar
• Balas E (1971) Intersection cuts—A new type of cutting planes for integer programming. Oper. Res. 19(1):19–39.Link, Google Scholar
• Balas E, Jeroslow RG (1980) Strengthening cuts for mixed integer programs. Eur. J. Oper. Res. 4(4):224–234.Crossref, Google Scholar
• Balas E, Perregaard M (2003) A precise correspondence between lift-and-project cuts, simple disjunctive cuts, and mixed integer Gomory cuts for 0–1 programming. Math. Programming 94(2–3):221–245.Crossref, Google Scholar
• Balas E, Saxena A (2008) Optimizing over the split closure. Math. Programming 113(2):219–240.Crossref, Google Scholar
• Balas E, Ceria S, Cornuéjols G (1996) Mixed 0–1 programming by lift-and-project in a branch-and-cut framework. Management Sci. 42(9):1229–1246.Link, Google Scholar
• Bixby RE, Ceria S, McZeal CM, Savelsbergh MWP (1998) An updated mixed integer programming library: MIPLIB 3.0. Optima 58:12–15.Google Scholar
• Bixby RE, Fenelon M, Gu Z, Rothberg E, Wunderling R (2000) MIP: Theory and practice—Closing the gap. Powell MJD, Scholtes S, eds. System Modelling and Optimization (Kluwer Academic Publisher, Boston), 19–49.Crossref, Google Scholar
• Bixby RE, Fenelon M, Gu Z, Rothberg E, Wunderling R (2004) Mixed-integer programming: A progress report. Grötschel M, ed., The Sharpest Cut: The Impact of Manfred Padberg and His Work (SIAM, Philadelphia), 309–325.Crossref, Google Scholar
• Bonami P (2012) On optimizing over lift-and-project closures. Math. Programming Comput. 4(2):151–179.Crossref, Google Scholar
• Caprara A, Letchford AN (2003) On the separation of split cuts and related inequalities. Math. Programming 94(2–3):279–294.Crossref, Google Scholar
• Caprara A, Fischetti M, Letchford AN (2000) On the separation of maximally violated mod-k cuts. Math. Programming 87(1): 37–56.Crossref, Google Scholar
• Cook WJ, Kannan R, Schrijver A (1990) Chvátal closures for mixed integer programming problems. Math. Programming 47(1–3):155–174.Crossref, Google Scholar
• Cornuéjols G, Nannicini G (2011) Practical strategies for generating rank-1 split cuts in mixed-integer linear programming. Math. Programming Comput. 3(4):281–318.Crossref, Google Scholar
• Dash S, Goycoolea M (2010) A heuristic to generate rank-1 GMI cuts. Math. Programming Comput. 2(3–4):231–257.Crossref, Google Scholar
• Dash S, Günlük O, Lodi A (2010) MIR closures of polyhedral sets. Math. Programming 121:33–60.Crossref, Google Scholar
• Dash S, Günlük O, Raack C (2011a) A note on the MIR closure and basic relaxations of polyhedra. Oper. Res. Lett. 39(1):198–199.Crossref, Google Scholar
• Dash S, Günlük O, Vielma JP (2011b) Computational experiments with cross and crooked cross cuts. Unpublished manuscript.Google Scholar
• Dey S, Lodi A, Tramontani A, Wolsey L (2010) Experiments with two row tableau cuts. Eisenbrand F, Shepherd FB, eds. Integer Programming and Combinatorial Optim., 14th Internat. Conf., IPCO 2010, Lausanne, Switzerland, June 9–11, 2010 . Proc., Lecture Notes in Computer Science, Vol. 6080 (Springer, Berlin), 424–437.Crossref, Google Scholar
• Fischetti M, Lodi A (2007) Optimizing over the first Chvàtal closure. Math. Programming 110(1):3–20.Crossref, Google Scholar
• Fischetti M, Salvagnin D (2011) A relax-and-cut framework for Gomory mixed-integer cuts. Math. Programming Comput. 3(2):79–102.Crossref, Google Scholar
• Fischetti M, Lodi A, Tramontani A (2011) On the separation of disjunctive cuts. Math. Programming 128(1–2):205–230.Crossref, Google Scholar
• Gomory RE (1963) An algorithm for integer solutions to linear programs. Graves RL, Wolfe P, eds. Recent Advances in Mathematical Programming (McGraw-Hill, New York), 269–302.Google Scholar
• Hiriart-Urruty J-B, Lemaréchal C (1996) Convex Analysis and Minimization Algorithms Part 1: Fundamentals (Springer-Verlag, Berlin).Google Scholar
• Laundy R, Perregaard M, Tavares G, Tipi H, Vazacopoulos A (2009) Solving hard mixed-integer programming problems with Xpress-MP: A MIPLIB 2003 case study. INFORMS J. Comput. 21(2):304–313.Link, Google Scholar
• Marchand H, Wolsey LA (2001) Aggregation and mixed integer rounding to solve MIPs. Oper. Res. 49(3):363–371.Link, Google Scholar
• Nemhauser GL, Wolsey L (1990) A recursive procedure to generate all cuts for 0–1 mixed integer programs. Math. Programming 46(1–3):379–390.Crossref, Google Scholar
• Wolter K (2006) Implementation of cutting plane separators for mixed integer programs. Master's thesis, Technische Universität Berlin, Berlin, Germany.Google Scholar