With the goal of obtaining strong relaxations for binary polynomial optimization problems, we introduce the pseudo-Boolean polytope defined as the convex hull of the set of binary points satisfying a collection of equations containing pseudo-Boolean functions. By representing the pseudo-Boolean polytope via a signed hypergraph, we obtain sufficient conditions under which this polytope has a polynomial-size extended formulation. Our new framework unifies and extends all prior results on the existence of polynomial-size extended formulations for the convex hull of the feasible region of binary polynomial optimization problems of degree at least three.

翻译：为获得二元多项式优化问题的强松弛，我们引入伪布尔多面体，其定义为满足包含伪布尔函数的方程组之二元点集的凸包。通过符号超图表示伪布尔多面体，我们获得了该多面体具有多项式规模扩展表述的充分条件。新框架统一并扩展了所有关于三次及以上二元多项式优化问题可行域凸包存在多项式规模扩展表述的现有结果。