Some New Convergence Results of Primal-Dual Hybrid Gradient Algorithm |
Published date:2014-12-15 Provided by:School of Science |
Title: Some New Convergence Results of Primal-Dual Hybrid Gradient Algorithm
Guest Speaker: Dr. Xiaoming Yuan (Hong Kong Baptist University) Time: 2014-12-18 (Thursday), 10:30 - 12:00 Abstract: The primal-dual hybrid gradient algorithm (PDHG) has been widely used, especially for some basic image processing models. In the literature, PDHG’s convergence was established only under some restrictive conditions on its step sizes. We will revisit PDHG’s convergence in the context of a saddle-point problem, and try to better understand how to choose its step sizes. More specifically, we will show by an extremely simple example that PDHG is not necessarily convergent when the step sizes are fixed as even tiny constants. We then show that PDHG with constant step sizes is indeed convergent if one of the functions of the saddle-point problem is strong convex, a condition that does hold for some variational models in imaging. With this additional condition, we also establish a worst-case convergence rate measured by the iteration complexity for PDHG with constant step sizes. Some extensions to total variational minimization models with finite element discretization will also be mentioned. Biography Xiaoming Yuan(袁晓明) was educated at Nanjing University (B.Sc., M.Phil.) and City University of Hong Kong (Ph.D.), all majoring in Mathematics. He had worked at University of Victoria, Shanghai Jiao Tong University, and University of British Columbia Okanagan before he joined Hong Kong Baptist University. |