Quadratic Transform for Fractional Programming in Signal Processing and Machine Learning: A unified approach for solving optimization problems involving ratios

作者：Kaiming Shen, Wei Yu · 发表于：IEEE Signal Processing Magazine · 年份：2025 · DOI：10.1109/msp.2025.3557958 · 被引用次数：2 · 研究领域：Advanced Control Systems Design、Optimization and Mathematical Programming、Advanced Optimization Algorithms Research

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 Cramér-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 thequadratic 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.