Local Linear Convergence of First-order Proximal Splitting Methods
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.
下午 14:00 ~ 15:00
Jingwei Liang, University of Cambridge