Efficient linear reformulations for binary polynomial optimization problems

We consider unconstrained polynomial minimization problems with binary variables (BPO). These can be easily linearized, i.e., reformulated into a MILP in higher dimensional space. Several linearizations are possible for given BPO, depending on how each monomial is decomposed and replaced by additional constraints. focus finding efficient that maximize the continuous relaxation bound of resulting MILP. For this purpose, we introduce notion linearization patterns allow us to model enumerate decompositions degree-d monomial. The assignment unique pattern BPO results reformulation Our method, called MaxBound, amounts searching an optimal association between monomials sense it leads best bound. show process formulated as which denote (MB˜). further highlight domination properties among discard dominated decrease size Another effect these now makes search requires few possible, based only non-dominated patterns. call method ND-MinVar again found solving another make experimental study degree 4 polynomials compares both methods shows advantages disadvantages each.