课程教学大纲
课程编号:G00TE1204
课程名称:凸优化及其在信号处理中的应用
课程英文名称:Convex Optimization and Its Applications in Signal Processing
开课单位:通信工程学院
教学大纲撰写人:苏文藻
课程学分:2学分
课内学时:32学时
课程类别:硕士/博士/专业学位
课程性质:任选
授课方式:讲课
考核方式:作业,考试
适用专业:通信与信息系统、信号与信息处理
先修课程:
教学目标:
同学应:
1.掌握建立基本优化模型技巧
2.掌握基本凸分析理论
3.掌握凸优化问
题
快递公司问题件快递公司问题件货款处理关于圆的周长面积重点题型关于解方程组的题及答案关于南海问题
的最优条件及对偶理论
4.认识凸优化在信号处理的一些应用
英文简介:
In this course we will develop the basic machineries for formulating and analyzing various optimization problems. Topics include convex analysis, linear and conic linear programming, nonlinear programming, optimality conditions, Lagrangian duality theory, and basics of optimization algorithms. Applications from signal processing will be used to complement the theoretical developments. No prior optimization background is required for this class. However, students should have workable knowledge in multivariable calculus, real analysis, linear algebra and matrix theory.
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课程主要内容:
Part I: Introduction
-Problem formulation
-Classes of optimization problems
Part II: Theory
-Basics of convex analysis
-Conic linear programming and nonlinear programming: Optimality conditions and duality theory
-Basics of combinatorial optimization
Part III: Selected Applications in Signal Processing
-Transmit beamforming
-Network localization
-Sparse/Low-Rank Regression
参考书目:
1.Ben-Tal, Nemirovski: Optimization I-II: Convex Analysis, Nonlinear Programming
Theory, Nonlinear Programming Algorithms, 2004.
2.Boyd, Vandenberghe: Convex Optimization, Cambridge University Press, 2004.
3.Luenberger, Ye: Linear and Nonlinear Programming (3rd Edition), 2008.
4.Nemirovski: Lectures on Modern Convex Optimization, 200
5.
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