标题： 一种用于带代数约束的全局非凸多项式优化的高效框架 显示英文标题

标题： An Efficient Framework for Global Non-Convex Polynomial Optimization with Algebraic Constraints

摘要： 我们提出了一种高效的框架，用于求解在超立方体子集上的代数约束全局非凸多项式优化问题。 我们证明了此类问题存在一种等价的非线性重写形式，该形式几乎没有任何虚假局部最小值。 通过在高维中以前难以处理的全局约束多项式优化问题上的数值实验，我们表明在计算最优值和位置时，可以实现维度和次数的多项式扩展。 显示英文摘要

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