2019年12月10日上午，波兰University of Zielona Góra Andrzej Cegielski教授受邀来南昌大学数学系访问交流，并在理生楼A502会议室为数学系师生作了题为“On the regularity of the Landweber transformation”的学术报告。数学系部分老师以及研究生参加了此次报告会，报告会由数学系唐玉超老师主持。

Cegielski教授主要介绍了Landweber变换算子的正则性质。首先Cegielski教授首先介绍了在求解非光滑优化问题中常见的非线性算子定义，包括非扩张、拟非扩张和强拟非扩张等，并给出了具体例子。然后回顾了求解分裂可行性问题的相关算法，并引出Landweber变换算子定义，指出现有的算法都可以看作是Landweber变换算子的特殊情形。进而，定义了三种Landweber变换算子的正则性质。同时，证明了一些具体算子的正则性质，基于所得结果，统一了现有一大类算法收敛性证明。在此基础上，Cegielski教授给出了一种参数化的Landweber变换算子定义，并证明其具有类似的正则性质等。最后，通过介绍若干数值算例，验证算法的有效性。报告结束后，Cegielski教授热情的回答了在座教师和同学提出的问题，并对共同感兴趣的问题展开了积极的讨论。

 

 

报告人简介：

Andrzej Cegielski, Full professor at University of Zielona Góra. He is the Dean of the Faculty of Mathematics, Computer Science and Econometrics between 2005 and 2012. His research interests including Iterative methods for convex optimization problems, Nondifferentiable minimization and Iterative methods for variational inequalities etc. Honors and Awards: Award of the Ministry of Science, Poland (1987), Award of the Rector of the University in Zielona Góra, Poland (1997, 2010, 2012, 2014,  2015, 2016, 2017, 2018), Award of the Rector of the Jagiellonian University (Mlak and Opial Award), Poland (2014). He is Vice President Polish Mathematical Society between 1999 and 2002. He is Member of Editorial Board of Discussiones Mathematicae. Differential Inclusions, Control and Optimization and Numerical Algorithms. He published over 36 peer reviewed papers in famous journals including SIAM Journal on Optimization, Inverse Problems, Optimization and Journal of Nonlinear and Convex Analysis, etc. He published an English written book, Iterative Methods for Fixed Point Problems in Hilbert Spaces, Lecture Notes in Mathematics 2057, Springer, Berlin, 2012.