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We consider lift-and-project methods for combinatorial optimization problems and focus mostly on those lift-and-project methods which generate polyhedral relaxations of the convex hull of integer solutions. We introduce many new variants of Sherali–Adams and Bienstock– Zuckerberg operators. These new operators fill the spectrum of polyhedral(More)
We study two polyhedral lift-and-project operators (originally proposed by Lovász and Schrijver in 1991) applied to the fractional stable set polytopes. First, we provide characterizations of all valid inequalities generated by these operators. Then, we present some seven-node graphs on which the operator enforcing the symmetry of the matrix variable is(More)
We consider operators acting on convex subsets of the unit hypercube. These operators are used in constructing convex relaxations of combinatorial optimization problems presented as a 0,1 integer programming problem or a 0,1 polynomial optimization problem. Our focus is mostly on operators that, when expressed as a lift-and-project operator, involve the use(More)
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