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

The pseudo-Boolean polytope and polynomial-size extended formulations for binary polynomial optimization