最佳化理論與應用

Convex optimization is a class of mathematical optimization problems, which includes least-square and linear programming problems that can be solved efficiently and arise in a variety of applications. The idea is to extend known tools for these two problems to a larger class of convex optimization problems, such as semidefinite programming. Convex optimization has found applications in many areas, such as estimation and signal processing, communications and networks, machine learning, circuit design, analysis, statistics, and finance, where it is used to find optimal or approximate solutions. The goal of this course is to develop a working knowledge for recognizing or formulating a problem as a convex optimization problem, which can then be reliably and efficiently solved by well developed numerical analysis tools.

A good knowledge of linear algebra and a basic understanding of probability theory and advanced analysis.

Lecture notes

Homework assignments 25% Midterm exams 35% Final exam 40%

• convex set
• convex function
• convex optimization problems
• duality
• unconstrained minimization
• equality constrained minimization
• interior-point methods
• course overview

Convex Optimization, Stephen Boyd and Lieven Vandenberghe, Cambridge University Press, 2004 Convex Optimization for Signal Processing and Communications: From Fundamentals to Applications, Chong-yung Chi, Wei-chiang Li, Chia-hsiang Lin (CRC Press, 2017)

地點

ED926

時間

Tue, 3:20pm-4:30pm

聯絡方式

Email: cylai@nctu.edu.tw