Numer. Math. Theor. Meth. Appl., 13 (2020), pp. 176-199.
Published online: 2019-12
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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} }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.