1
课程详述
COURSE SPECIFICATION
以下课程信息可能根据实际授课需要或在课程检讨之后产生变动。如对课程有任何疑问，请联
系授课教师。
The course information as follows may be subject to change, either during the session because of unforeseen
circumstances, or following review of the course at the end of the session. Queries about the course should be
directed to the course instructor.
1.
课程名称 Course Title
凸优化算法 Algorithms for convex optimization
2.
授课院系
Originating Department
数学系 Department of Mathematics
3.
课程编号
Course Code
MAT7028
4.
课程学分 Credit Value
3
5.
课程类别
Course Type
专业选修课 Major Elective Courses
6.
授课学期
Semester
7.
授课语言
Teaching Language
中文 Chinese
8.
授课教师、所属学系、联系方
式（如属团队授课，请列明其
他授课教师）
Instructor(s), Affiliation&
Contact
（For team teaching, please list
all instructors）
何炳生教授；张振助理教授
Bingsheng He, Professor; Zhen Zhang, Assistant Professor
9.
实验员/助教、所属学系、联系
方式
Tutor/TA(s), Contact
10.
选课人数限额(可不填)
Maximum Enrolment
（Optional）
授课方式
Delivery Method
讲授
Lectures
习题/辅导/讨论
Tutorials
实验/实习
Lab/Practical
其它(请具体注明)
Other（Please specify）
总学时
Total
11.
学时数
Credit Hours
2
12.
先修课程、其它学习要求
Pre-requisites or Other
Academic Requirements
MA103b 线性代数 I
MA103b Linear algebra I.
13.
后续课程、其它学习规划
Courses for which this course
is a pre-requisite
14.
其它要求修读本课程的学系
Cross-listing Dept.
教学大纲及教学日历 SYLLABUS
15.
教学目标 Course Objectives
Optimization problems arising from big data problem, dimension reduction, machine learning, image
processing and etc, can be translated and/or relaxed to a large scale structured convex optimization. This
course is devoted for the students interested in solving practical large optimization problems in the different
areas of science and technology.
For solving the large scale problems, it is recognized that the first order algorithms is practical and relative
effective. The alternating direction method of multipliers (ADMM) is a benchmark for solving a linearly
constrained convex minimization model with a two-block separable objective function. In this course, we
will introduce the new development of the ADMM-like methods, both in theoretical convergence, and the
practical implementations and applications.
最优化理论与方法是运筹学与计算数学的交叉学科。近 20 年来, 信号处理, 图像恢复, 机器学习等
信息技术领域以及统计学、数据科学中涌现了大量的优化问题. 有效地求解这些问题, 是当今一些世
界一流应用数学家关切的课题, 也是应用数学的一个新的研究热点。
数据科学中大规模计算问题的很大一部分可以归结为（或松弛成）一个可分离算子的凸优化问题.
由于问题规模大, 传统的优化求解方法往往难以凑效. 根据问题的结构特点, 设计简单易行的一阶分裂
算法已渐成学界共识。
变分不等式是运筹学中许多问题的一种统一表述模式. 经济活动中的最优平衡问题、政策性调
控问题, 都可以用变分不等式来描述. 最优化和变分不等式有着紧密的联系. 凸优化的一阶最优性条
件就是一个单调变分不等式. 在变分不等式的框架下考虑凸优化的求解方法, 就像微积分中用导数
求一元二次函数的极值, 常常会带来很大的方便。
本课程中介绍凸规划的分裂收缩算法, 始终追求简单统一的原则， 都纳入统一的框架. 统一框架揭
示方法之间的内在联系, 简化算法的收敛性证明, 又能对设计新的算法, 提高算法效率提供指导性帮
助.
16.
预达学习成果 Learning Outcomes
3
17.
课程内容及教学日历 （如授课语言以英文为主，则课程内容介绍可以用英文；如团队教学或模块教学，教学日历须注明
主讲人）
Course Contents (in Parts/Chapters/Sections/Weeks. Please notify name of instructor for course section(s), if
this is a team teaching or module course.)
Section 1
Introduction for convex optimization and monotone variational inequality 6 Hours
Section 2
Projection and contraction methods for monotone variational inequalities 6 Hours
Section 3
Customized Proximal Point Algorithms and Relaxed PPA for linearly constrained
optimization. 6Hours
Section 4
Alternating direction methods of multiplies for structured convex optimization 6 Hours
Section 5
New developments of ADMM 6 Hours
Section 6
Study of the Convergence rate of the splitting methods 6 Hours
Section 7
ADMM-like methods for multi-blocks linearly constrained convex optimization 6 Hours
Section 8
Splitting contraction in a unified framework. 6 Hours
18.
教材及其它参考资料 Textbook and Supplementary Readings
自编教材， 主要内容取自 (http://math.nnju.edu.cn/~hebma)上《凸优化和单调变分不等式的收缩算
法》
EnglishVersion: (http://maths.nnju.edu.cn/~hebma) Lectures of 'Contraction Methods for Convex
Optimization and Monotone Variational Inequalities'
参考书籍： Stephen Boyd and Lieven Vandenberghe， Convex Optimization
课程评估 ASSESSMENT
19.
评估形式
Type of
Assessment
评估时间
Time
占考试总成绩百分比
% of final
score
违纪处罚
Penalty
备注
Notes
出勤 Attendance
课堂表现
Class
Performance
小测验
Quiz
4
课程项目 Projects
平时作业
Assignments
期中考试
Mid-Term Test
期末考试
Final Exam
60%
期末报告
Final
Presentation
其它（可根据需要
改写以上评估方
式）
Others (The
above may be
modified as
necessary)
Programming
(40%)
20.
记分方式 GRADING SYSTEM
课程审批 REVIEW AND APPROVAL
21.
本课程设置已经过以下责任人/委员会审议通过
This Course has been approved by the following person or committee of authority
