A recursive procedure to generate all cuts for 0-1 mixed integer programs
Mathematical Programming: Series A and B
Chva´tal closures for mixed integer programming problems
Mathematical Programming: Series A and B
Optimizing over the split closure
Mathematical Programming: Series A and B
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
Operations Research Letters
Certificates of linear mixed integer infeasibility
Operations Research Letters
A probabilistic comparison of the strength of split, triangle, and quadrilateral cuts
Operations Research Letters
Approximating the Split Closure
INFORMS Journal on Computing
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Many cuts used in practice to solve mixed integer programs are derived from a basis of the linear relaxation. Every such cut is of the form αTx≥1, where x≥0 is the vector of non-basic variables and α≥0. For a point $\bar{x}$ of the linear relaxation, we call αTx≥1 a zero-coefficient cut wrt. $\bar{x}$ if $\alpha^T \bar{x} = 0$, since this implies αj=0 when $\bar{x}_j 0$. We consider the following problem: Given a point $\bar{x}$ of the linear relaxation, find a basis, and a zero-coefficient cut wrt. $\bar{x}$ derived from this basis, or provide a certificate that shows no such cut exists. We show that this problem can be solved in polynomial time. We also test the performance of zero-coefficient cuts on a number of test problems. For several instances zero-coefficient cuts provide a substantial strengthening of the linear relaxation.