Department of Mathematics
Convergence analysis of primal-dual algorithms for a saddle-point problem: From contraction perspective
Recently, some primal-dual algorithms have been proposed for solving a saddle-point problem, with particular applications in the area of total variation image restoration. This paper focuses on the convergence analysis of these primal-dual algorithms and shows that their involved parameters (including step sizes) can be significantly enlarged if some simple correction steps are supplemented. Some new primal-dual-based methods are thus proposed for solving the saddle-point problem. We show that these new methods are of the contraction type: the iterative sequences generated by these new methods are contractive with respect to the solution set of the saddle-point problem. The global convergence of these new methods thus can be obtained within the analytic framework of contraction-type methods. The novel study on these primal-dual algorithms from the perspective of contraction methods substantially simplifies existing convergence analysis. Finally, we show the efficiency of the new methods numerically. © 2012 Society for Industrial and Applied Mathematics.
Contraction method, Image restoration, Primal-dual method, Proximal point algorithm, Saddle point problem, Total variation
Source Publication Title
SIAM Journal on Imaging Sciences
Society for Industrial and Applied Mathematics
He, Bingsheng, and Xiaoming Yuan. "Convergence analysis of primal-dual algorithms for a saddle-point problem: From contraction perspective." SIAM Journal on Imaging Sciences 5.1 (2012): 119-149.