@Article{NMTMA-13-176, author = {Bai , JianchaoLi , Jicheng and Wu , Zhie}, title = {Several Variants of the Primal-Dual Hybrid Gradient Algorithm with Applications}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2019}, volume = {13}, number = {1}, pages = {176--199}, abstract = {

By reviewing the primal-dual hybrid gradient algorithm (PDHG) proposed 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 previous. By making use of variational analysis, the global convergence and sublinear convergence rate in the ergodic/nonergodic sense are established, and the  numerical efficiency of our algorithms is verified by testing an image deblurring problem compared with several existing algorithms.

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.OA-2019-0030}, url = {http://global-sci.org/intro/article_detail/nmtma/13436.html} }