Study of the polytope of the \({{\,\mathrm{at \text{-} least}\,}}\) predicate

  • Niko Kaso
  • Serge KrukEmail author
Original Article


Constraint programming is a powerful tool for modeling various problems in operations research. Its strength lies in the use of predicates, or global high-level constraints, on a few variables to efficiently model complex and varied problem structures. In this paper, we consider the predicate at-least. It bounds the number of variables in a set that may receive a specific value. This is a generalization of the standard logic condition expressed when the sum of binary variables is expressing a lower bound on the cardinality of a set. We have completely determined the convex hull representation of this predicate and provide a polynomial separation algorithm for inclusion in branch-and-bound integer programming software.


Constraint programming At-least predicate Facet-inducing inequalities Separation algorithm 



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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsOakland UniversityRochesterUSA

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