Computational Experiments with Cross and Crooked Cross Cuts

References

• Andersen K, Louveaux Q, Weismantel R, Wolsey LA (2007) Inequalities from two rows of a simplex tableau. Fischetti M, Williamson DP, eds. IPCO, Lecture Notes in Computer Science, Vol. 4513 (Springer, Berlin), 1–15.Crossref, Google Scholar
• Balas E (1979) Disjunctive programming. Ann. Discrete Math. 5:3–51.Crossref, Google Scholar
• Balas E, Bonami P (2009) Generating lift-and-project cuts from the LP simplex tableau: Open source implementation and testing of new variants. Math. Programming Comput. 1:165–199.Crossref, Google Scholar
• Balas E, Saxena A (2008) Optimizing over the split closure. Math. Programming 113:219–240.Crossref, Google Scholar
• Balas E, Ceria S, Cornuéjols G, Natraj N (1996) Gomory cuts revisited. Oper. Res. Lett. 19:1–9.Crossref, Google Scholar
• Basu A, Bonami P, Cornuéjols G, Margot F (2011) Experiments with two-row cuts from degenerate tableaux. INFORMS J. Comput. 23:578–590.Link, Google Scholar
• Basu A, Conforti M, Cornuéjols G, Zambelli G (2010) Minimal inequalities for an infinite relaxation of integer programs. SIAM J. Discrete Math. 24:158–168.Crossref, Google Scholar
• Bixby ER, Ceria S, McZeal CM, Savelsbergh MWP (1998) An updated mixed integer programming library: MIPLIB 3.0. Optima 58:12–15.Google Scholar
• Bixby ER, 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, IFIP the International Federation for Information Processing, Vol. 46 (Springer, Berlin), 19–49.Crossref, Google Scholar
• Bonami P (2012) On optimizing over lift-and-project closures. Math. Programming Comput. 4:151–179.Crossref, Google Scholar
• Bonami P, Cornuéjols G, Dash S, Fischetti M, Lodi A (2008) Projected Chvátal–Gomory cuts for mixed integer linear programs. Math. Programming 113:241–257.Crossref, Google Scholar
• Borozan V, Cornuéjols G (2009) Minimal valid inequalities for integer constraints. Math. Oper. Res. 34:538–546.Link, Google Scholar
• Conforti M, Cornuéjols G, Zambelli G (2011a) Corner polyhedron and intersection cuts. Surveys Oper. Res. Management Sci. 16:105–120.Crossref, Google Scholar
• Conforti M, Cornuéjols G, Zambelli G (2011b) A geometric perspective on lifting. Oper. Res. 59:569–577.Link, Google Scholar
• Cook W, Kannan R, Schrijver A (1990) Chvátal closures for mixed integer programming problems. Math. Programming 47:155–174.Crossref, Google Scholar
• Dash S (2010) On the complexity of cutting-plane proofs using split cuts. Oper. Res. Lett. 38:109–114.Crossref, Google Scholar
• Dash S, Goycoolea M (2010) A heuristic to generate rank-1 GMI cuts. Math. Programming Comput. 2:231–257.Crossref, Google Scholar
• Dash S, Günlük O (2006) Valid inequalities based on simple mixed-integer sets. Math. Programming 105:29–53.Crossref, Google Scholar
• Dash S, Günlük O (2008) On the strength of Gomory mixed-integer cuts as group cuts. Math. Programming 115:387–407.Crossref, Google Scholar
• Dash S, Dey SS, Günlük O (2011) On mixed-integer sets with two integer variables. Oper. Res. Lett. 39:305–309.Crossref, Google Scholar
• Dash S, Dey SS, Günlük O (2012a) Two-dimensional lattice-free cuts and asymmetric disjunctions for mixed-integer polyhedra. Math. Programming 135:221–254.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, Molinaro M (2012b) On the relative strength of different generalizations of split cuts. IBM Technical Report RC25326, IBM, Yorktown Heights, NY.Google Scholar
• Dey SS, Tramontani A (2009) Recent developments in multi-row cuts. Optima 80:2–8.Google Scholar
• Dey SS, Wolsey LA (2010a) Constrained infinite group relaxations of MIPs. SIAM J. Optim. 20:2890–2912.Crossref, Google Scholar
• Dey SS, Wolsey LA (2010b) Two-row mixed-integer cuts via lifting. Math. Programming 124:143–174.Crossref, Google Scholar
• Dey SS, Lodi A, Tramontani A, Wolsey LA (2010) Experiments with two-row tableau cuts. Eisenbrand F, Shepherd FB, eds. IPCO, Lecture Notes in Computer Science, Vol. 6080 (Springer, Berlin), 424–437.Crossref, Google Scholar
• Espinoza DG (2010) Computing with multi-row Gomory cuts. Oper. Res. Lett. 38:115–120.Crossref, Google Scholar
• Fischetti M, Salvagnin D (2011) A relax-and-cut framework for Gomory mixed-integer cuts. Math. Programming Comput. 3:79–102.Crossref, Google Scholar
• Fischetti M, Saturni C (2007) Mixed-integer cuts from cyclic groups. Math. Programming 109:27–53.Crossref, Google Scholar
• Fischetti M, Lodi A, Tramontani A (2011) On the separation of disjunctive cuts. Math. Programming 128:205–230.Crossref, Google Scholar
• Fukasawa R, Goycoolea M (2011) On the exact separation of mixed integer knapsack cuts. Math. Programming 128:19–41.Crossref, Google Scholar
• Fukasawa R, Günlük O (2011) Strengthening lattice-free cuts using nonnegativity. Discrete Optim. 8:229–245.Crossref, Google Scholar
• Li Y, Richard J-PP (2008) Cook, Kannan and Schrijvers's example revisited. Discrete Optim. 5:724–734.Crossref, Google Scholar
• Louveaux Q, Poirrier L (2012) An algorithm for the separation of two-row cuts. Math. Programming 143(1–2):111–146.Crossref, Google Scholar