【开课说明】

Lecturer: Prof. Kazufumi Ito 
举办日期：2020年07月06日 ~ 07月17日
举办地点：ZOOM会议室
主办单位：国家天元数学中部中心、武汉大学数学与统计学院
课时数： 30课时
授课时间：07.06~07.10  07.13~07.17   08:30-11:00  

【报名流程及联系人】

1. 通过Email提交报名申请，附件报名表电子版见本页面底部（文件命名格式为“20200706短期课程报名表+学员姓名+学校名”）；
2. 邮件发至：tmcc@whu.edu.cn，邮件主题为“20200706短期课程报名申请”;
3. 报名截止日期为2020年06月30日，以电子邮件收信时间为准，我们将邮件回复每一位录取的学员。
4. 联系人：杨老师

电话：027-87778085 / 16602740903    Email:tmcc@whu.edu.cn

【课程介绍】

In this course we discuss nonsmooth optimization problems arising in various areas of science and engineering. We develop the optimization theory and algorithms for a general class of variational problems. Applications are presented and analyzed for various examples inlcuding control and design optimization, inverse problem, image analysis and variational problems. Non-convex and non-smooth optimization becomes increasingly important for the advanced and effective use of optimization methods and thus theory are essential tools for mathematical modeling and analysis, We introduce basic function space and functional analysis tools need for the course.

The course provides an introduction to functional spaces and convex analysis and their basic concepts with illustrated examples. A general class of constrained optimization problems in function spaces is discussed and we develop the Lagrange multiplier theory and effective solution algorithms, Emerging applications of nonsmooth optimization include the image analysis, the classification and machine learning, the Bayesian statistics, and the mean-field analysis. We apply the optimization theory to analyze sparsity optimization and non-convex optimization and constrained PDE optimization problems and to treat such applications. Thus, the course provides the basic materials for nonsmooth optimization as well as how the theory and algorithms are put to use for advanced applications.