Fractional programming (FP) is a branch of mathematical optimization that deals with the optimization of ratios. It is an invaluable tool for signal processing and machine learning, because many key metrics in these fields are fractionally structured, e.g., the signal-to-interference-plus-noise ratio (SINR) in wireless communications, the Cram\'{e}r-Rao bound (CRB) in radar sensing, the normalized cut in graph clustering, and the margin in support vector machine (SVM). This article provides a comprehensive review of both the theory and applications of a recently developed FP technique known as the quadratic transform, which can be applied to a wide variety of FP problems, including both the minimization and the maximization of the sum of functions of ratios as well as matrix-ratio problems.

翻译：分式规划是数学优化的一个分支，主要研究比率形式的优化问题。该工具在信号处理与机器学习领域具有重要价值，因为这些领域的许多关键指标都具有分式结构，例如无线通信中的信干噪比、雷达感知中的克拉美-罗界、图聚类中的归一化割，以及支持向量机中的间隔。本文系统综述了近年来发展的分式规划技术——二次变换方法——的理论与应用，该技术可广泛应用于各类分式规划问题，包括分式和函数的极小化与极大化问题，以及矩阵比值问题。