报告人：徐洪坤（杭州电子科技大学）

时间：5月26日9:30-11:00

地点：36-304

摘要：Iterative methods are an essential part of nonlinear analysis and optimization. Projection methods are the fundamental iterative methods, which were traced back to John von Neumann (1903-1957) who introduced in 1933 the projection method by proving the strong convergence of the alternating projection procedure to a common point in the intersection of two closed subspaces of a Hilbert space. In 1937, Stefan Kaczmarz (1895-1939) introduced a projection method, now known as Kaczmarz algorithm, for solving a linear system. This method remained, however, unnoticed for over 30 years until the 70th of the 20th century, when it turned out that the method could have a lot of applications in various areas of mathematics as well as many practical applications in physics, medicine, the computerized tomography, and many other imaging technologies. In 1951, Landweber introduced a projection method for solving linear integral equations of the first kind. Landweber's method is now one of the most popular methods for linear and nonlinear inverse problems.In this talk we discuss the convergence analysis of projection methods, including some historical results and current advances. We will also mention some applications of projection methods for feasibility and optimization problems such as split feasibility problem and compressive sensing.

报告人简介：徐洪坤，杭州电子科技大学特聘教授，南非科学院院士，发展中国家科学院（TWAS）院士；西安交通大学博士，加拿大Dalhousie大学博士后；曾任华东理工大学副教授，西班牙塞维利亚大学访问教授，南非夸祖鲁-纳塔尔大学教授与资深教授，沙特国王大学教授，天津市特聘讲座教授，台湾中山大学西湾讲席教授,、数学系主任和理学院经理；曾获南非数学会杰出研究奖，教育部自然科学二等奖，陕西高等学校科学技术奖一等奖；受聘为浙江省特聘专家，建有浙江省院士专家工作站。研究兴趣和领域包括非线性分析与优化理论、算法及其在机器学习中的应用，数据分析的数学基础以及拓扑和几何数据分析，非线性算子方程和反问题正则化理论的迭代方法，巴拿赫空间几何理论及其非线性映射不动点理论和算法，金融数学等。发表论文280余篇。任20余种国际数学期刊编委/副主编/主编，入选汤森路透/科睿唯安全球高被引学者，爱思唯尔中国高被引学者，斯坦福全球前2%顶尖科学家年度和生涯影响力双榜单，Research.com全球千名数学家榜单。