報告題目：An inexact Uzawa algorithmic framework for nonlinear saddle point problems with applications to elliptic optimal control problem
報 告 人：宋永存博士 香港大學
報告時間：2020年6月18日下午 1:30-2:30
報告地點：騰訊會議 ID：368 452 008
會議密碼：061820
點擊鍊接入會，或添加至會議列表：https://meeting.tencent.com/s/sN0cwS0DQvj6
校内聯系人：張凱 zhangkaimath@jlu.edu.cn
報告摘要：
We consider a class of nonlinear saddle point problems with various applications in PDEs and optimal control problems, and propose an algorithmic framework based on some inexact Uzawa methods in the literature. Under mild conditions, the convergence of this algorithmic framework is uniformly proved and the linear convergence rate is estimated. We take an elliptic optimal control problem with control constraints as an example to illustrate how to choose application-tailored preconditioners to generate specific and efficient algorithms by the algorithmic framework. The resulting algorithm does not need to solve any optimization subproblems or systems of linear equations in its iteration; each of its iterations only requires the projection onto a simple admissible set, four algebraic multigrid V-cycles, and a few matrix-vector multiplications. Its numerical efficiency is then demonstrated by some preliminary numerical results.
報告人簡介：
Yongcun Song is now a PhD student at the Department of Mathematics, The University of Hong Kong, after he graduated from Jilin University in 2016. His research area includes numerical optimization, operator splitting algorithms, and optimal control problems. He won the best paper prize in the 5th Graduate Forum of the Mathematical Programming Branch of Operational Research Society of China.
