DB004225-凸优化理论方法

研究生课程开设申请表

开课院（系、所）：信息科学与工程学院       

课程申请开设类型： 新开     重开□     更名□（请在□内打勾，下同）

一、课程介绍（含教学目标、教学要求等）（300字以内）

近二十年来，随着凸优化理论趋于成熟、高效优化算法不断涌现及各种信息设备计算能力大幅度提升，凸优化理论及方法已成为包括无线/有线通信、信号处理、电路设计、自动控制、金融工程、交通、物流等几乎所有工程领域最重要的数学工具之一。本课程主要面向（但不限于）通信与信息工程专业的硕士研究生和博士研究生，系统的介绍凸优化理论方法及其应用。课程的主要内容包括背景及基础知识、凸优化基础理论与算法以及凸优化在通信和信号处理方面的应用几个部分。本课程将培养研究生运用凸优化理论与算法解决相关领域科研问题的能力。

二、教学大纲（含章节目录）：（可附页）

本课程包括三个主要部分：

1. 背景及基础知识

   • 课程介绍及相关基础知识：背景知识介绍及线性代数、概率知识补充

2. 凸优化基础理论与算法

   • 凸集合与凸函数：凸集合与凸函数定义及保持凸特性运算

   • 凸优化问题：凸优化问题定义，LP、SOCP、SDP等凸问题，问题等价变换

   • 拉格朗日对偶及KKT条件：最小准则、拉格朗日、对偶问题、KKT条件

   • 凸优化算法及软件：梯度算法、牛顿算法、内点算法及CVX软件

3. 凸优化应用

   • 窄带及宽带（OFDM）通信系统优化：窄带及宽带接收机设计与功率分配

   • 单用户MIMO通信系统优化：MIMO接收机设计，收发机联合优化

   • 多用户MIMO通信系统优化：多用户上行、下行收发机设计

   • 半正定规划及其应用：SDP及其在波束成形与检测方面应用

   • 鲁棒性优化：最坏情况鲁棒性优化与统计鲁棒性优化及其应用

   • 分解算法及其应用：基于凸优化的dual/primal分解算法及其应用

   • 非凸优化问题及SCA与MM算法：连续凸逼近（SCA）与Majorization-Minimization算法

三、教学周历

注：1.以上一、二、三项内容将作为中文教学大纲，在研究生院中文网页上公布，四、五内容将保存在研究生院。2.开课学期为：春季、秋季或春秋季。3.授课语言为：汉语、英语或双语教学。4.适用学科范围为：公共，一级，二级，三级。5.实践环节为：实验、调研、研究报告等。6.教学方式为：讲课、讨论、实验等。7.学位课程考试必须是笔试。8.课件地址指在网络上已经有的课程课件地址。9.主讲教师简介主要为基本信息（出生年月、性别、学历学位、专业职称等）、研究方向、教学与科研成果，以100至500字为宜。

四、主讲教师简介：

王家恒，洪堡（高级）学者，IEEE高级会员，教授，博士生导师。2001年和2006年于东南大学无线电工程系获得学士和硕士学位，2010年于香港科技大学电子与计算机工程系获得博士学位，2010年至2011年期间在瑞典皇家工学院信号处理实验室从事博士后研究工作，自2011年任教于东南大学移动通信国家重点实验。长期从事无线通信和信号处理系统优化设计方面工作，研究方向包括：5G/6G移动通信系统、MIMO/大规模MIMO传输、密集异构网络、无线光通信、毫米波通信、区块链技术、机器学习、边缘计算、鲁棒性设计、分布式算法设计、绿色通信、协作通信、认知无线电等。发表学术论文140余篇，包括IEEE、OSA等国际权威期刊（SCI）论文90余篇。

五、任课教师信息（包括主讲教师）：

六、课程开设审批意见

说明：1．研究生课程重开、更名申请也采用此表。表格下载：http:/seugs.seu.edu.cn/down/1.asp

2．此表一式三份，交研究生院、院（系）和自留各一份，同时提交电子文档交研究生院。

Application Form For Opening Graduate Courses

School (Department/Institute)：

Course Type: New Open    Reopen □   Rename □（Please tick in □, the same below）

1. Course Introduction (including teaching goals and requirements) within 300 words:

During the recent two decades, with the development of convex optimization theory and methods as well as enhanced computational capacity of various information devices, convex optimization has become one of the most important mathematical tools in almost all engineering areas such as wireless/wireline communications, signal processing, circuit designs, automatic control, finance engineering, traffic engineering, logistics and etc. This course aims to systematically introduce convex optimization theory and methods to doctor and master graduate students majoring in (but not limited) communications and information engineering. The course is composed several parts including the background and preliminary knowledge, fundamental theory and methods of convex optimization, and advanced applications of convex optimization. Through this course, the capability of the students to address research problems using convex optimization will be trained.

2. Teaching Syllabus (including the content of chapters and sections. A sheet can be attached):

 This course contains three main parts:

1. background and preliminary knowledge

   •  Course introduction and preliminary knowledge: introduce some background and preliminary knowledge such as linear algebra and probabilities.

2. Fundamental theory and methods of convex optimization

   •  Convex sets and convex functions: the definitions of convex sets and functions and related operations.

   •  Convex optimization problems: the definition of convex problems, LP, SOCP, SDP formulations, equivalent transformations.

   •  Lagrange duality and KKT conditions: minimum principle, Lagrange, dual problems, and KKT conditions.

   •  Convex optimization algorithms and software: gradient algorithms, Newton algorithm, interior-point algorithm and CVX.

3. Advanced applications of convex optimization

   •  Narrow-band and broad-band (OFDM) communication system optimization: receiver designs and power allocation.

   •  Single-user MIMO communication system optimization: MIMO receiver designs and transceiver designs.

   •  Multi-user MIMO communication system optimization: multi-user uplink and downlink transceiver designs.

   •  Semidefinite programing and its applications: SDP and its applications in beamforming and detection.

   •  Robust optimization: worst-case robust and statistically robust optimization and their applications.

   •  Decomposition algorithms and their applications: dual/primal decomposition algorithms and their applications.

   •  Nonconvex optimization problems via SCA and MM algorithms: Successive convex approximation and majorization-minimization algorithms.

3. Teaching Schedule:

 Note: 1.Above one, two, and three items are used as teaching Syllabus in Chinese and announced on the Chinese website of Graduate School. Thefour and five items are preserved in Graduate School.

 2. Course terms: Spring, Autumn , and Spring-Autumn term.  

 3. The teaching languages for courses: Chinese, English or Chinese-English.

 4.Applicable range of discipline: public, first-class discipline, second-class discipline, and third-class discipline.

 5. Practice includes: experiment, investigation, research report,etc.

 6. Teaching methods: lecture, seminar, practice, etc.

 7. Examination for degree courses must be in paper.

 8.Teaching material websitesarethose which have already been announced.

 9. Brief introduction of chief lecturer should include: personal information (date of birth, gender, degree achieved, professional title), research direction, teaching and research achievements. (within 100-500 words)

4. Brief Introduction of Chief lecturer:

Jiaheng Wang received the Ph.D. degree in electronic and computer engineering from the Hong Kong University of Science and Technology, Kowloon, Hong Kong, in 2010, and the B.E. and M.S. degrees from the Southeast University, Nanjing, China, in 2001 and 2006, respectively.

He is currently a Full Professor at the National Mobile Communications Research Laboratory (NCRL), Southeast University, Nanjing, China. From 2010 to 2011, he was with the Signal Processing Laboratory, KTH Royal Institute of Technology, Stockholm, Sweden. He also held visiting positions at the Friedrich Alexander University Erlangen-Nürnberg, Nürnberg, Germany, and the University of Macau, Macau. His research interests include optimization in signal processing and wireless communications.

Dr. Wang has published more than 140 articles on international journals and conferences. From 2014 to 2018, he served as an Associate Editor for the IEEE Signal Processing Letters. From 2018, he serves as a Senior Area Editor for the IEEE Signal Processing Letters. He was a recipient of the Humboldt Fellowship for Experienced Researchers and the best paper awards of IEEE GLOBECOM 2019, ADHOCNETS 2019, and WCSP 2014.

5. Lecturer Information (include chief lecturer)