Theory of linear and integer programming
Theory of linear and integer programming
Chva´tal closures for mixed integer programming problems
Mathematical Programming: Series A and B
Mathematical Programming: Series A and B
Combinatorial optimization
Generalized Convex Disjunctive Programming: Nonlinear Convex Hull Relaxation
Computational Optimization and Applications
Split closure and intersection cuts
Mathematical Programming: Series A and B
Cuts for mixed 0-1 conic programming
Mathematical Programming: Series A and B
Perspective cuts for a class of convex 0–1 mixed integer programs
Mathematical Programming: Series A and B
Optimizing over the first Chvátal closure
Mathematical Programming: Series A and B
Optimizing over the split closure
Mathematical Programming: Series A and B
Cuts for Conic Mixed-Integer Programming
IPCO '07 Proceedings of the 12th international 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
Branching and bounds tighteningtechniques for non-convex MINLP
Optimization Methods & Software - GLOBAL OPTIMIZATION
Conic mixed-integer rounding cuts
Mathematical Programming: Series A and B
MIR closures of polyhedral sets
Mathematical Programming: Series A and B
Lifting inequalities: a framework for generating strong cuts for nonlinear programs
Mathematical Programming: Series A and B
Perspective relaxation of mixed integer nonlinear programs with indicator variables
IPCO'08 Proceedings of the 13th international conference on Integer programming and combinatorial optimization
Disjunctive cuts for non-convex mixed integer quadratically constrained programs
IPCO'08 Proceedings of the 13th international conference on Integer programming and combinatorial optimization
Binary positive semidefinite matrices and associated integer polytopes
IPCO'08 Proceedings of the 13th international conference on Integer programming and combinatorial optimization
Optimizing over the first chvàtal closure
IPCO'05 Proceedings of the 11th international conference on Integer Programming and Combinatorial Optimization
A constructive characterization of the split closure of a mixed integer linear program
Operations Research Letters
The submodular knapsack polytope
Discrete Optimization
An algorithmic framework for convex mixed integer nonlinear programs
Discrete Optimization
The Chvátal-Gomory Closure of a Strictly Convex Body
Mathematics of Operations Research
On the Chvátal-Gomory closure of a compact convex set
IPCO'11 Proceedings of the 15th international conference on Integer programming and combinatoral optimization
The Gomory-Chvátal Closure of a Nonrational Polytope Is a Rational Polytope
Mathematics of Operations Research
Facial structure and representation of integer hulls of convex sets
IPCO'13 Proceedings of the 16th international conference on Integer Programming and Combinatorial Optimization
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It is well-know that the Chvátal-Gomory (CG) closure of a rational polyhedron is a rational polyhedron. In this paper, we show that the CG closure of a bounded full-dimensional ellipsoid, described by rational data, is a rational polytope. To the best of our knowledge, this is the first extension of the polyhedrality of the CG closure to a non-polyhedral set. A key feature of the proof is to verify that all non-integral points on the boundary of ellipsoids can be separated by some CG cut. Given a point u on the boundary of an ellipsoid that cannot be trivially separated using the CG cut parallel to its supporting hyperplane, the proof constructs a sequence of CG cuts that eventually separates u. The polyhedrality of the CG closure is established using this separation result and a compactness argument. The proof also establishes some sufficient conditions for the polyhedrality result for general compact convex sets.