We present an efficient framework for solving constrained global non-convex polynomial optimization problems. We prove the existence of an equivalent nonlinear reformulation of such problems that possesses essentially no spurious local minima. We show through numerical experiments that polynomial scaling in dimension and degree is achievable for computing the optimal value and location of previously intractable global constrained polynomial optimization problems in high dimension.

翻译：我们提出了一种高效框架，用于求解带约束的全局非凸多项式优化问题。我们证明了此类问题存在一种本质上无虚假局部极小值的等价非线性重构形式。通过数值实验表明，在计算高维中先前难以处理的全局约束多项式优化问题的最优值与最优位置时，可实现维数与度数的多项式级缩放。