摘要
By reviewing the primal-dual hybrid gradient algorithm(PDHG)pro-posed by He,You and Yuan(SIAM J.Image Sci.,7(4)(2014),pp.2526–2537),in this paper we introduce four improved schemes for solving a class of saddle-point problems.Convergence properties of the proposed algorithms are ensured based on weak assumptions,where none of the objective functions are assumed to be strongly convex but the step-sizes in the primal-dual updates are more flexible than the pre-vious.By making use of variational analysis,the global convergence and sublinear convergence rate in the ergodic/nonergodic sense are established,and the numer-ical efficiency of our algorithms is verified by testing an image deblurring problem compared with several existing algorithms.
基金
The work is partly supported by the NSF of China(No.11671318)
the NSF of Fujian province(No.2016J01028).
