题目：Quasi-Variational Inequalities: Semismooth Newton, Optimal Control, and Uncertainties

时间：2024年12月10日（周二）下午 2: 30-3: 30

地点：数学院203

报告人：Prof. Michael Hintermüller

邀请人：陈亮

摘要: This talk presents recent advances on the development of globally convergent semismooth Newton methods in function space for solving a class of quasi-variational inequalities (QVIs) associated with elliptic partial differential operators and obstacle-type constraints. Due to the possible set-valuedness of the solution map, selection principles such as retrieving the minimal or maximal solution are discussed and analyzed. The latter also turn out to be useful in the context of optimal control of QVIs. Finally, data uncertainty is studied and associated stationarity characterizations for optimal control problems of the associated QVI are derived. The talk ends by a number of numerical illustrations.

报告人简介：Michael Hintermüller is currently the director of Weierstrass Institute for Applied Analysis and Stochastics and the Chair Professor of Applied Mathematics in Humboldt University of Berlin. Among a couple of prominent positions, he is also the Chair of Berlin Mathematics Research Center named MATH+, which is one of the three Excellence Clusters in Mathematics funded by German Science Foundation (DFG).  Michael Hintermüller received his Ph.D. degree in technical mathematics from the University of Linz, Austria, in 1997. He had a Postdoctoral position and an Assistant Professor position at the University of Graz, where he got his Habilitation in Mathematics in 2003. From 2003 to 2004, he held a visiting Associate Professorship at Rice University, Houston, and an Associate Professorship at the University of Graz from 2004–2007. From 2007 to 2008, he held a Chair in Applied Mathematics at the University of Sussex, U.K. In 2008, he became a MATHEON Research Professor and a W3-Professor in Applied Mathematics at the Department of Mathematics of Humboldt-University of Berlin, Germany.

He has won several important prizes and honours, e.g., in 2005, he received the prestigious START-prize from the Austrian Ministry of Science and Education; in 2006, he got a SIAM Outstanding Paper Prize; he was a Young Member of Austrian Academy of Sciences from 2009 - 2017, and was elected as SIAM Fellow in 2016. He is currently or was on the editorial board of many important journals in applied and computational mathematics, including SIOPT, Math. Program., SINUM, SISC for example.

His main research areas are optimization with partial differential equation constraints, mathematical image processing, inverse problems and problems in shape and topology optimization.