Stanford EE364A - Convex Optimization I - Boyd

Catalog description Concentrates on recognizing and solving convex optimization problems that arise in applications. Convex sets, functions, and optimization problems. Basics of convex analysis. Least-squares, linear and quadratic programs, semidefinite programming, minimax, extremal volume, and other problems. Optimality conditions, duality theory, theorems of alternative, and applications. Interior-point methods. Applications to signal processing, statistics and machine learning, control and mechanical engineering, digital and analog circuit design, and finance. Course objectives to give students the tools and training to recognize convex optimization problems that arise in applications to present the basic theory of such problems, concentrating on results that are useful in computation to give students a thorough understanding of how such problems are solved, and some experience in solving them to give students the background required to use the methods in their own research work or

本目录专注于识别和解决在实际应用中出现的凸优化问题。涵盖凸集、函数与优化问题。凸分析的初步知识。最小二乘法、线性与二次规划、半定规划、极值理论、极值体积及其他问题。最优性条件、对偶理论、交替定理及其应用。内点法。应用于信号处理、统计学与机器学习、控制与机械工程、数字与模拟电路设计，以及金融领域。课程目标在于向学生提供识别应用中出现的凸优化问题的工具与训练，介绍此类问题的基本理论，侧重于对计算有用的结果，使学生深入理解此类问题的解决方法，并积累解决此类问题的经验，同时为学生提供在自身研究工作中运用这些方法所需的背景知识。