报 告 人：Martin J. Gander

　　报告地点：数学与统计学院104室

　　报告时间：2014年11月13日星期四15:30

　　报告简介：The history of constrained optimization spans nearly three centuries. It goes back to a letter Johann Bernoulli sent in 1715 to Varignon, announcing a very simple rule with which the many hundreds of different problems in fluid and solid mechanics considered in detail by Varignon can be solved in the blink of an eye. Varignon then explains this rule at the end of his book, but unfortunately cites the letter of Johann Bernoulli with an incorrect date. Bernoulli's rule, based on virtual velocities, was later carefully explained by Lagrange, and led to the discovery of the famous multiplier method of Lagrange, with which many optimization problems can be easily treated. Using so called Lagrange multipliers is however a much more far reaching concept, and we will see that one can, armed only with Lagrange multipliers, discover the important primal and dual equations in optimal control and the famous maximum principle of Pontryagin. Pontryagin himself however did not discover his maximum principle using Lagrange multipliers, he used a more geometric argument. We will finally give the complete formulation of PDE constrained optimization based on duality introduced by Lions.

　　主讲人简介：

　　Martin J. GANDER is a full professor at department of mathematics, University of Geneva, Switzerland; and an adjunct professor of Mathematics at McGill University, Montreal, Canada. He received Diploma (M.S.) in computer science from ETH Zürich (Switzerland) at 1993, M.S. in Mathematics from Stanford University (USA) at 1995, and Ph.D. in Scientific Computing and Computational Mathematics from Stanford University (USA) at 1997. His scientific interests are Domain Decomposition Methods, Waveform Relaxation Methods, Parallel Space Time Methods, Preconditioning, etc. From 2006 to 2011, he was in the editorial board of SIAM Review. Now he is in the editorial boards for seven scientific journals, e.g. SIAM Journal on Scientific Computing, Numerical Algorithms. In addition, he is the president of the International Scientific Committee on Domain Decomposition Methods. Up to now, he has published more than 100 papers in peer-reviewed journals and conference proceedings, such as SIAM Rev., SIAM J. Sci. Comput., SIAM J. Numer. Anal., SIAM J. Matrix Anal., Math. Comp., J. Comput. Acoust., BIT. He is cited for 727 times by 409 authors in the MR citation database (up to Oct. 20, 2014).