The Sum-of-Squares (SOS) approximation method is a technique used in optimization problems to derive lower bounds to the optimal value of an objective function. By representing the objective function as a sum of squares in a feature space, the SOS method transforms non-convex global optimization problems into solvable semidefinite programs. This note presents an overview of the SOS method. We start with its application in finite-dimensional feature spaces and, subsequently, we extend it to infinite-dimensional feature spaces using kernels (k-SOS). Additionally, we highlight the utilization of SOS for estimating some relevant quantities in information theory, including the log-partition function.

翻译：平方和逼近方法是一种用于优化问题的技术，旨在推导目标函数最优值的下界。通过在特征空间中将目标函数表示为平方和形式，SOS方法可将非凸全局优化问题转化为可解的半定规划问题。本文对SOS方法进行了综述。首先介绍其在有限维特征空间中的应用，随后利用核方法将其扩展至无限维特征空间（k-SOS）。此外，我们重点阐述了SOS方法在估计信息理论中若干重要量值（包括对数配分函数）方面的应用。