在学生已经掌握运筹学和运营管理基本内容的基础上,本课程将进一步介绍运筹学和运营管理的高阶分析方法,即凸优化
理论及其应用。本课程旨在为学生提供识别商业和工程应用中出现的非线性优化问题的训练,介绍基本的理论知识,并专
注于建模方面和应用中有用的结果。凸优化是解决大规模问题的核心工具,本课程从凸优化的角度涵盖数学规划和组合优
化。 主要内容包括凸集、凸函数、优化问题、半定规划、对偶理论和鲁棒优化。 介绍了优化理论在机器学习、经济学和
统计学的应用。
After students have learned the basic knowledge of operations research and operations management, this course will
further introduce an advanced analysis method in operations research and operations management, namely convex
optimization theory and its applications. This course aims to give students the training to recognize nonlinear
optimization problems that arise in business and engineering applications, presenting the basic theory, and
concentrating on modeling aspects and results that are useful in applications. The course covers mathematical
programming and combinatorial optimization from the perspective of convex optimization, which is a central tool for
solving large-scale problems. Topics include convex sets, convex functions, optimization problems, semidefinite
programming, duality theory and robust optimization. Applications to machine learning, economics, and statistics are
presented.
1. 了解非线性和凸优化的基本概念和知识
2. 有能力建立并且分析非线性优化问题
3. 具有使用求解器解决一般优化问题的能力
1. Understand the basic concepts and knowledge regarding nonlinear and convex optimization
2. Have the capability to formulate and analyze nonlinear optimization problems
3. Have the capability to solve general optimization problems using different solvers
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.)