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
A hierarchy of relaxation between the continuous and convex hull representations
SIAM Journal on Discrete Mathematics
A lift-and-project cutting plane algorithm for mixed 0-1 programs
Mathematical Programming: Series A and B
Mixed 0-1 programming by lift-and-project in a branch-and-cut framework
Management Science
When Does the Positive Semidefiniteness Constraint Help in Lifting Procedures?
Mathematics of Operations Research
Cutting Planes and the Elementary Closure in Fixed Dimension
Mathematics of Operations Research
Bounds on the Chvátal Rank of Polytopes in the 0/1-Cube
Proceedings of the 7th International IPCO Conference on Integer Programming and Combinatorial Optimization
On the Matrix-Cut Rank of Polyhedra
Mathematics of Operations Research
Some Fundamental Properties of Successive Convex Relaxation Methods on LCP and Related Problems
Journal of Global Optimization
On the Rank of Mixed 0, 1 Polyhedra
Proceedings of the 8th International IPCO Conference on Integer Programming and Combinatorial Optimization
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
On the MIR Closure of Polyhedra
IPCO '07 Proceedings of the 12th international conference on Integer Programming and Combinatorial Optimization
The integer hull of a convex rational polytope
ICCSA'03 Proceedings of the 2003 international conference on Computational science and its applications: PartIII
DRL*: A hierarchy of strong block-decomposable linear relaxations for 0-1 MIPs
Discrete Applied Mathematics
Split Rank of Triangle and Quadrilateral Inequalities
Mathematics of Operations Research
A relax-and-cut framework for gomory's mixed-integer cuts
CPAIOR'10 Proceedings of the 7th international conference on Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems
On the rank of cutting-plane proof systems
IPCO'10 Proceedings of the 14th international conference on Integer Programming and Combinatorial Optimization
Exact MAX-2SAT solution via lift-and-project closure
Operations Research Letters
Note: On the polyhedral lift-and-project methods and the fractional stable set polytope
Discrete Optimization
Strengthening Chvátal-Gomory cuts and Gomory fractional cuts
Operations Research Letters
Hi-index | 0.00 |
In integer programming, the elementary closure associated with a family of cuts is the convex set defined by the intersection of all the cuts in the family. In this paper, we compare the elementary closures arising from several classical families of cuts: three versions of Gomory's fractional cuts, three versions of Gomory's mixed integer cuts, two versions of intersection cuts and their strengthened forms, Chvatal cuts, MIR cuts, lift-and-project cuts without and with strengthening, two versions of disjunctive cuts, Sherali-Adams cuts and Lovasz-Schrijver cuts with positive semi-definiteness constraints.