Simple odd beta-cycle inequalities for binary polynomial optimization

We consider the multilinear polytope which arises naturally in binary polynomial optimization. Del Pia and Di Gregorio introduced the class of odd beta-cycle inequalities valid for this polytope, showed that these generally have Chv├ítal rank 2 with respect to the standard relaxation and that, together with flower inequalities, they yield a perfect formulation for cycle … Read more

A smaller extended formulation for the odd cycle inequalities of the stable set polytope

For sparse graphs, the odd cycle polytope can be used to compute useful bounds for the maximum stable set problem quickly. Yannakakis introduced an extended formulation for the odd cycle inequalities of the stable set polytope in 1991, which provides a direct way to optimize over the odd cycle polytope in polynomial time, although there … Read more

The Multilinear polytope for acyclic hypergraphs

We consider the Multilinear polytope defined as the convex hull of the set of binary points satisfying a collection of multilinear equations. Such sets are of fundamental importance in many types of mixed-integer nonlinear optimization problems, such as binary polynomial optimization. Utilizing an equivalent hypergraph representation, we study the facial structure of the Multilinear polytope … Read more

A new family of facet defining inequalities for the maximum edge-weighted clique problem

This paper considers a family of cutting planes, recently developed for mixed 0-1 polynomial programs and shows that they define facets for the maximum edge-weighted clique problem. There exists a polynomial time exact separation algorithm for these in- equalities. The result of this paper may contribute to the development of more efficient algorithms for the … Read more