We consider the multilinear polytope defined as the convex hull of the set of binary points z,
satisfying a collection of equations of the form ze=∏ v∈ ezv for all e∈ E. The complexity of …

We consider the multilinear polytope which arises naturally in binary polynomial
optimization. Del Pia and Di Gregorio introduced the class of odd β-cycle inequalities valid …

In this work, we advance the understanding of the fundamental limits of computation for
binary polynomial optimization (BPO), which is the problem of maximizing a given …

We consider unconstrained polynomial minimization problems with binary variables (BPO).
These problems can be easily linearized, ie, reformulated into a MILP in a higher …

In this paper, we study the problem of minimizing a polynomial function with literals over all
binary points, often referred to as pseudo-Boolean optimization. We investigate the …

With the goal of obtaining strong relaxations for binary polynomial optimization problems, we
introduce the pseudo-Boolean polytope defined as the set of binary points z∈{0, 1} V∪ S …

We consider the problem of inference in higher-order undirected graphical models with
binary labels. We formulate this problem as a binary polynomial optimization problem and …

Fundamental to many applications in data analysis are the decompositions of a graph, ie
partitions of the node set into component-inducing subsets. One way of encoding …

It is well-known that the McCormick relaxation for the bilinear constraint z= xy gives the
convex hull over the box domains for x and y. In network applications where the domain of …

In this paper we extend the core branch-and-bound algorithm of an RLT-based solver for
continuous polynomial optimization, RAPOSa, to handle mixed-integer problems. We do so …