课程名称：Convex Optimization and its Applications

课程编号：0212148

课程性质：任选课

学 分：2学分

学 时：30学时

招收对象：博士研究生（限额30人）

开课教授：罗智泉教授（美国明尼苏达大学）

上课时间：5月6日、5月8日、5月10日, 5月13日、5月15日、5月17日、5月20日、5月22日、5月24日,每天上午9:00-11:30

上课地点：新科技楼1602

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General Description: This course will provide students with mathematical tools and training to deal with optimization problems in engineering. It will introduce basic convex optimization models and robust optimization techniques. All concepts and theories will be illustrated with numerous applications from signal processing, digital communication (wireless communication system design), control, and circuit design. A main objective is to teach students how to give good and robust formulations to engineering problems in a way that is amenable to efficient solution by modern optimization algorithms. This course is intended to provide a core optimization background for undergraduate/graduate students from such areas like applied mathematics, signal and image processing, communications, control, CAD, robotics, structural analysis, computer graphics, algorithms & complexity, computational geometry.

Recommended Reference:

1. S. Boyd and L. Vandenberghe, Convex Optimization. Cambridge University Press.

2. D. Bertsekas, Nonlinear Programming. Athena Scientific.

Prerequisites: Mathematical maturity, comfortable with linear algebra, probability theory , analysis. Exposure to Matlab , numerical optimization ,and application fields helpful but not required.

Tentative Course Outline:

1. Lecture 1: Introduction, convex sets and functions

2. Lecture 2: Linear, quadratic and conic optimization

3. Lecture 3: Duality theory

4. Lecture 4: Interior point methods

5. Lecture 5: Introduction to complexity theory