Integer and combinatorial optimization
Integer and combinatorial optimization
The Boolean quadric polytope: some characteristics, facets and relatives
Mathematical Programming: Series A and B
The equipartition polytope. I: formulations, dimension and basic facets
Mathematical Programming: Series A and B
The equipartition polytope. II: valid inequalities and facets
Mathematical Programming: Series A and B
Chva´tal cuts and odd cycle inequalities in quadratic 0–1 optimization
SIAM Journal on Discrete Mathematics
Cut-polytopes, Boolean quadratic polytopes and nonnegative quadratic pseudo-Boolean functions
Mathematics of Operations Research
Mathematical Programming: Series A and B
A lower bound for a constrained quadratic 0-1 minimization problem
Discrete Applied Mathematics
Cardinality constrained Boolean quadratic polytope
Proceedings of the 4th Twente workshop on Graphs and combinatorial optimization
On the dimension of projected polyhedra
Discrete Applied Mathematics
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In this paper we consider the problem of optimizing a quadratic pseudo-Boolean function subject to the cardinality constraint Σ1 ≤ i ≤ n xi = k with a polyhedral method. More precisely we propose a study of the convex hull of feasible points included in the Padberg's Boolean quadric polytope and satisfying the cardinality constraint. Specifically, we investigate the connection with the Boolean quadric polytope and study a facet family. The relationship with two other polytopes of the literature is also explored.