An Exponential Lower Bound on the Length of Some Classes of Branch-and-Cut Proofs
Proceedings of the 9th International IPCO Conference on Integer Programming and Combinatorial Optimization
Exponential Lower Bound for Static Semi-algebraic Proofs
ICALP '02 Proceedings of the 29th International Colloquium on Automata, Languages and Programming
Complexity of Semi-algebraic Proofs
STACS '02 Proceedings of the 19th Annual Symposium on Theoretical Aspects of Computer Science
Computation of the Lasserre Ranks of Some Polytopes
Mathematics of Operations Research
Discrete Applied Mathematics
IPCO'11 Proceedings of the 15th international conference on Integer programming and combinatoral optimization
Design and verify: a new scheme for generating cutting-planes
IPCO'11 Proceedings of the 15th international conference on Integer programming and combinatoral optimization
Towards optimal integrality gaps for hypergraph vertex cover in the lovász-schrijver hierarchy
APPROX'05/RANDOM'05 Proceedings of the 8th international workshop on Approximation, Randomization and Combinatorial Optimization Problems, and Proceedings of the 9th international conference on Randamization and Computation: algorithms and techniques
On the rank of cutting-plane proof systems
IPCO'10 Proceedings of the 14th international conference on Integer Programming and Combinatorial Optimization
Random half-integral polytopes
Operations Research Letters
Approximate formulations for 0-1 knapsack sets
Operations Research Letters
On the complexity of cutting-plane proofs using split cuts
Operations Research Letters
Note: On the polyhedral lift-and-project methods and the fractional stable set polytope
Discrete Optimization
Tree-width and the Sherali-Adams operator
Discrete Optimization
Elementary closures for integer programs
Operations Research Letters
Handelman rank of zero-diagonal quadratic programs over a hypercube and its applications
Journal of Global Optimization
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Lov脙隆sz and Schrijver (1991) described a semidefinite operator for generating strong valid inequalities for the 0-1 vectors in a prescribed polyhedron. Among their results, they showed thatn iterations of the operator are sufficient to generate the convex hull of 0-1 vectors contained in a polyhedron inn-space. We give a simple example, having Chv脙隆tal rank 1, that meets this worst case bound ofn. We describe another example requiringn iterations even when combining the semidefinite and Gomory-Chv脙隆tal operators. This second example is used to show that the standard linear programming relaxation of ak-city traveling salesman problem requires at least ? k/8? iterations of the combined operator; this bound is best possible, up to a constant factor, ask+1 iterations suffice.