课程代码

Course Code

MATH6015

*学时

Teaching Hours

48

*学分

Credits

3

*课程名称

Course Name

最优化方法

Optimization Method

*授课语言

Instruction Language

英语

English

*开课院系

School

中英国际低碳学院

China-UK Low Carbon College

先修课程

Prerequisite

线性代数，程序设计，数值分析

Linear algebra, Programming, Numerical analysis

授课教师

Instructors

姓名Name

职称Title

单位Department

联系方式E-mail

鞠生宏

Shenghong Ju

副教授

Associate Professor

中英国际低碳学院

China-UK Low Carbon College

shenghong.ju@sjtu.edu.cn

*课程简介（中文）Course Description

最优化理论是基础与应用数学的一个重要分支，涉及面广（例如线性代数、实分析、拓扑学、数列、凸分析，以及微分学等），在许多领域有重要的一席之地：自然科学、计算机科学、管理科学、工业工程等。最优化问题主要是通过在给定范围里选取变量数值，找出问题的最优解决方案（例如，多变量实值函数最大化或最小化）。最优化结果以及基于结果的预测的质量取决于模型的相关性、算法的效率，以及数值处理的方法。本课程主要授课内容涵盖三大类，包括：无约束优化(一维搜索、梯度优化算法、信赖域方法)、约束优化(罚函数法、二次规划、拉格朗日乘子法)和智能优化算法(遗传算法、模拟退火、粒子群优化、贝叶斯优化等算法)。通过以上内容的介绍，学生将掌握最优化的基本理论，了解常用算法的收敛性理论，熟悉各类优化问题的算法。授课过程同时着重引导学生运用Matlab、Python等数学工具进行优化建模，设立了优化竞赛项目，加深学生对最优化理论和算法的理解，增强解决实际优化问题的能力。

*课程简介（English）Course Description

Optimization is a branch of fundamental and applied mathematics. It is based on several fields of mathematics (e.g., linear algebra, real analysis, topology, number sequence, convex analysis and differential calculus), and plays an important role in many application fields: natural science, computer science, management science, industry and engineering etc. An optimization problem consists of finding a best solution of a problem (e.g., maximizing or minimizing a multivariate real valued function) by choosing variables in a given domain. The quality of the results and the predictions depends on the relevance of the model, the efficiency of the algorithm and the methods for numerical processing. This course covers the unconstrained optimization (one-dimensional search, gradient optimization algorithm, and trust region method), constrained optimization (penalty function method, quadratic programming, and Lagrange multiplier method) and intelligent optimization algorithms (genetic algorithm, simulated annealing, particle swarm optimization, Bayesian optimization). Through this course, students are expected to master the basic theory of optimization, understand the convergence theory of commonly used algorithms, and be familiar with algorithms for various optimization problems. The teaching process also guide students to use Matlab and Python mathematical tools to do optimize modeling. An optimization competition project is set up to strengthen the students' understanding of the optimization theory and algorithms, and enhance the ability to solve practical optimization problems.

*教学安排

Schedules

教学内容Content

授课学时

Hours

教学方式

Format

授课教师

Instructor

Introduction to Optimization: Course details, definition, method classification, optimization competition project

最优化方法概述：课程安排、相关定义、方法分类、优化竞赛介绍

3

Lecture

S. Ju

Unconstrained optimization method: Line search

无约束优化：一维搜索

3

Lecture

S. Ju

Unconstrained optimization method: Steepest descent method, Newton method

无约束优化：最速下降法，牛顿法

3

Lecture

S. Ju

Unconstrained optimization method: Quasi-Newton method, Conjugate gradient method

无约束优化：拟牛顿法、共轭梯度法

3

Lecture

S. Ju

Unconstrained optimization method: Trust-region method

无约束优化：信赖域方法

3

Lecture

S. Ju

Unconstrained optimization method: review, computer experiment

无约束优化方法复习回顾、上机实验

3

Computer experiment

S. Ju

Constrained optimization method: Penalty method

约束优化：罚函数法

3

Lecture

S. Ju

Constrained optimization method: Quadratic programming

约束优化：二次规划

3

Lecture

S. Ju

Constrained optimization method: Lagrange multiplier method

约束优化：拉格朗日乘子法

3

Lecture

S. Ju

Constrained optimization method: review, computer experiment

约束优化复习回顾、上机实验

3

Computer experiment

S. Ju

Intelligent optimization algorithms: Genetic Algorithm, computer experiment

智能优化：遗传算法、上机实验

3

Lecture + computer experiment

S. Ju

Intelligent optimization algorithms: Simulated Annealing, computer experiment

智能优化：模拟退火优化、上机实验

3

Lecture + computer experiment

S. Ju

Intelligent optimization algorithms: Particle Swarm Optimization, computer experiment

智能优化：粒子群优化、上机实验

3

Lecture + computer experiment

S. Ju

Intelligent optimization algorithms: Bayesian Optimization, computer experiment

智能优化：贝叶斯优化、上机实验

3

Lecture + computer experiment

S. Ju

优化竞赛：获胜者演讲

Optimization competition: winner presentations

3

Lecture

S. Ju

Final exam

期末考试

3

Exam

S. Ju

*考核方式Grading Policy

出勤：5%, 平时作业：15%, 优化竞赛: 20%, 期末考试：60%

Attendance 5%, Homework 15%, Optimization competition 20%, Final exam 60%

*教材或参考资料Textbooks & References

1. 陈宝林，最优化理论与算法（第2版），清华大学出版社，2005.

2. 许国根，赵后随，黄智勇，最优化方法及其MATLAB实现，北京航空航天大学出版社，2018.

3. Jorge Nocedal, Stephen J. Wright, Numerical Optimization, Springer New York, 2006.

4. Mykel J. Kochenderfer, Tim A. Wheeler, Algorithms for Optimization, Illustrated Edition, The MIT Press, 2019.

5. Singiresu S. Rao. Engineering Optimization: Theory and Practice, Fourth Edition, John Wiley & Sons, Inc, 2009.

备注

Notes