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Subspace Descent Method

Xiaozhe Hu, Associate Professor(Tufts University)
Tuesday, August 11th, 2020, 8:00 PM  腾讯会议ID:363 713 546
主持人:朱升峰 副教授
报告地点:腾讯会议ID:363 713 546(无密码) https://meeting.tencent.com/s/EAFlfeNTjOsB

报告摘要:In this work, we propose an optimization algorithm based on subspace decomposition. Our subspace descent (SD) method is inspired by the method of subspace corrections. The efficiency of the method relies on the condition number of the problem is small when measured in a proper chosen norm and a space decomposition which is stable in this norm. Under cetain assumptions, we derive the convergence results for both cyclic and random ordering SD. We also show that (block) coordinate descent method from the optimization community and full approximation storage scheme from numerical PDE community can be analyzed under the SD framework. Preliminary numerical experiments are presented to demonstrate the effectiveness of the SD method. This is joint work with Long Chen, Steven Wise, and Huiwen Wu.

报告人简介:Xiaozhe Hu is an Associate Professor in the Department of Mathematics at Tufts University. He received his Ph.D. in Computational Mathematics from Zhejiang University in 2009. He conducted a year of postdoctoral research at the Beijing International Center of Mathematical Research and then became a postdoctoral fellow in the Department of Mathematics at Pennsylvania State University in 2010. He served in the position of Research Assistant Professor at Penn State before joining Tufts in 2014. Hu’s primary research interests are in numerical analysis and scientific computing, with an emphasis on the development, analysis, and implementation of numerical algorithms for solving partial differential equations and graph problems arising from different applications, such as multiphase flow in porous media, magnetohydrodynamics, bioinformatics, and machine learning. His algorithms have been used by commercial companies such as NVIDIA, China National Offshore Oil Company, and Petro-China. In 2016, his work received the Reimann-Liouville Award at the International Conference on Fractional Differentiation and Its Applications and his algorithm won the best performer of Disease Module Identification DREAM Challenges. He was a plenary speaker at the twenty-fourth International Conference on Domain Decomposition Methods in 2017. His research has been supported by the U.S. Department of Energy and the National Science Foundation. He?serves?as?an?Associate Editor for Journals: Numerical Linear Algebra with Application,Petroleum Science, etc.
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