Theory of linear and integer programming
Theory of linear and integer programming
Inequalities from Two Rows of a Simplex Tableau
IPCO '07 Proceedings of the 12th international conference on Integer Programming and Combinatorial Optimization
On the facets of mixed integer programs with two integer variables and two constraints
Mathematical Programming: Series A and B
Minimal Valid Inequalities for Integer Constraints
Mathematics of Operations Research
Computing with multi-row gomory cuts
IPCO'08 Proceedings of the 13th international conference on Integer programming and combinatorial optimization
Mixed-integer sets from two rows of two adjacent simplex bases
Mathematical Programming: Series A and B - Series B - Special Issue: Combinatorial Optimization and Integer Programming
On a generalization of the master cyclic group polyhedron
Mathematical Programming: Series A and B
Minimal Inequalities for an Infinite Relaxation of Integer Programs
SIAM Journal on Discrete Mathematics
Constrained Infinite Group Relaxations of MIPs
SIAM Journal on Optimization
On degenerate multi-row Gomory cuts
Operations Research Letters
Split Rank of Triangle and Quadrilateral Inequalities
Mathematics of Operations Research
On Maximal $S$-Free Convex Sets
SIAM Journal on Discrete Mathematics
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In recent years there has been growing interest in generating valid inequalities for mixed-integer programs using sets with two or more constraints. In particular, Andersen et al. (2007) [2] and Borozan and Cornuejols (2009) [3] have studied sets defined by equations that contain exactly one integer variable per row. The integer variables are not restricted in sign. Cutting planes based on this approach have already been computationally studied by Espinoza (2008) [8] for general mixed-integer problems, and there is ongoing computational research in this area. In this paper, we extend the model studied in the earlier papers and require the integer variables to be non-negative. We extend the results in [2] and [3] to our case, and show that cuts generated by their approach can be strengthened by using the non-negativity of the integer variables. In particular, it is possible to obtain cuts which have negative coefficients for some variables.