We prove that computing approximate stationary points of min-max optimization over the hypercube is PPAD-hard for quadratic polynomials. This holds even when the polynomials are multilinear, each variable appears in at most three monomials, and the approximation factor is inverse polynomial. As a direct consequence, we obtain the first PPAD-hardness results for two-team zero-sum polymatrix games.

翻译：我们证明，在超立方体上计算二次多项式极小极大优化的近似驻点是PPAD-难的。即使多项式是多重线性的，每个变量最多出现在三个单项式中，且近似因子为逆多项式，该结论仍然成立。作为直接推论，我们得到了两个团队零和多项式矩阵博弈的首个PPAD-难结果。