An efficient method for adapting step-size parameters of primal-dual hybrid gradient method in application to total variation regularization

Primal-dual hybrid gradient (PDHG) method is a very important technique for convex optimization which has a lot of applications in signal processing such as total variation regularization. It is efficient for low-computational cost of update procedures and relatively faster convergence compared with only primal or dual method. However, the difficulty for selecting a primal and a dual step-size parameters is well-known as its critical bottleneck. In this paper, we propose a new adaptive step- size parameter selection method for PDHG which is a modified version of a technique proposed by Goldstein et al. in 2015. A great improvement of convergence speed was shown in our experiments.