This course aims to teach the fundamental principles of convex optimization and its broad applications. Through systematic study, students will master the basic knowledge of convex sets, convex functions, and convex optimization problems, becoming familiar with the core tools and techniques of convex analysis. They will learn to identify, formulate, and solve practical convex optimization problems, covering topics such as least-squares, linear and quadratic programming, semidefinite programming, minimax problems, extremal volume problems, optimality conditions, and duality theory. Additionally, the course introduces modern optimization algorithms like interior-point methods and applies theoretical knowledge to practical case studies in fields such as signal processing, statistics and machine learning, control and mechanical engineering, digital and analog circuit design, and finance. By completing this course, students will gain comprehensive knowledge and skills in
convex optimization, providing a solid foundation for further academic research or practical work. |
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