Chva´tal closures for mixed integer programming problems
Mathematical Programming: Series A and B
MIP: Theory and Practice - Closing the Gap
Proceedings of the 19th IFIP TC7 Conference on System Modelling and Optimization: Methods, Theory and Applications
A Computational Study of Search Strategies for Mixed Integer Programming
INFORMS Journal on Computing
The Art of Computer Programming, Volume 4, Fascicle 3: Generating All Combinations and Partitions
The Art of Computer Programming, Volume 4, Fascicle 3: Generating All Combinations and Partitions
Operations Research Letters
Operations Research Letters
On the relative strength of split, triangle and quadrilateral cuts
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Minimal Valid Inequalities for Integer Constraints
Mathematics of Operations Research
Split Rank of Triangle and Quadrilateral Inequalities
Mathematics of Operations Research
Experiments with Two-Row Cuts from Degenerate Tableaux
INFORMS Journal on Computing
Maximal Lattice-Free Polyhedra: Finiteness and an Explicit Description in Dimension Three
Mathematics of Operations Research
Experiments with two row tableau cuts
IPCO'10 Proceedings of the 14th international conference on Integer Programming and Combinatorial Optimization
On degenerate multi-row Gomory cuts
Operations Research Letters
Computing with multi-row Gomory cuts
Operations Research Letters
Strengthening lattice-free cuts using non-negativity
Discrete Optimization
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Cutting planes for mixed integer problems (MIP) are nowadays an integral part of all general purpose software to solve MIP. The most prominent, and computationally significant, class of general cutting planes are Gomory mixed integer cuts (GMI). However finding other classes of general cuts for MIP that work well in practice has been elusive. Recent advances on the understanding of valid inequalities derived from the infinite relaxation introduced by Gomory and Johnson for mixed integer problems, has opened a new possibility of finding such an extension. In this paper, we investigate the computational impact of using a subclass of minimal valid inequalities from the infinite relaxation, using different number of tableau rows simultaneously, based on a simple separation procedure.We test these ideas on a set of MIPs, including MIPLIB 3.0 and MIPLIB 2003, and show that they can improve MIP performance even when compared against commercial software performance.