2018-12-24 | Jingwei Liang:一阶近似分裂法的局部线性收敛性



First-order proximal splitting methods are widely used in many fields through science and engineering, such as compressive sensing, signal/image processing, data science, machine learning and statistics, to name a few. The goal of this talk is to establish the local convergence analysis of first-order methods when the involved functions are partly smooth relative to an active manifold. We show that all these methods correctly identify the active manifolds in finite time, and then enter a local linear convergence regime, which is characterize precisely based on the geometry of the underlying smooth manifold. The obtained result is verified by several concrete numerical experiments arising from compressed sensing, signal/image processing and machine learning.






Jingwei Liang is currently a postdoc research associate at Department of Applied Mathematics and Theoretical Physics, University of Cambridge. He obtained his PhD in applied mathematics from Normandy University France. Before that, he received his master degree in applied mathematics in 2013 from Shanghai Jiao Tong University, and bachelor degree in Electronic and Information Engineering from Nanjing University of Posts and Telecommunications. His current research interests mainly focus on non-smooth optimization and signal/image processing.