报告题目：A Space Decomposition Framework for Nonlinear Optimization
报 告 人：Zaikun Zhang, Assistant Professor, Hong Kong Polytechnic University
报告时间：2020 年9 月25 日上午 10：10-10：45
报告地点：腾讯会议 ID：870 938 043
Space decomposition has been a popular methodology in both the community of optimization and that of numerical PDEs. Under the name of Domain Decomposition Methods, the latter community has developed highly successful techniques like Restricted Additive Schwarz and Coarse Grid. Being crucial for the performance of Domain Decomposition Methods, these techniques are however less studied in optimization. This talk presents a framework that allows us to extend these techniques to general nonlinear optimization. We establish the global convergence and convergence rate of the framework. Numerical results, although preliminary, show the Restricted Additive Schwarz and Coarse Grid (now Coarse Space) techniques can effectively accelerate space decomposition methods as they do in Domain Decomposition Methods.
This is a joint work with Serge Gratton (ENSEEIHT/INPT, University of Toulouse) and Luis Nunes Vicente (Liehigh University).
Dr. Zaikun Zhang is an assistant professor at the Hong Kong Polytechnic University. He obtained his Bachelor’s degree from the School of Mathematics, Jilin University in 2007, and PhD degree from the Chinese Academy of Sciences in 2012. Then he worked at University of Coimbra and INP-ENSEEIHT, University of Toulouse as a postdoctoral researcher. He joined the Hong Kong Polytechnic University in 2016.
The research interests of Zaikun Zhang include derivative-free optimization, optimization based on inaccurate information, randomized methods, and decomposition methods. He is the PI of a PROCORE - France/Hong Kong Joint Research project, a Hong Kong RGC Early Career Scheme project, and a Hong Kong RGC General Research Fund project. His research is published in journals including Mathematical Programming, SIAM Journal on Optimization, and SIAM Journal on Scientific Computing.