Convergence analysis for a primal-dual monotone + skew splitting algorithm with applications to total variation minimization
For researchers in optimization and image processing, this provides theoretical guarantees and acceleration for a known algorithm, but the contributions are incremental.
This paper analyzes the convergence of a primal-dual splitting method for monotone inclusions, deriving convergence rates for convex minimization and proposing accelerated schemes under strong monotonicity. Applications to total variation-based image restoration are demonstrated.
In this paper we investigate the convergence behavior of a primal-dual splitting method for solving monotone inclusions involving mixtures of composite, Lipschitzian and parallel sum type operators proposed by Combettes and Pesquet in [7]. Firstly, in the particular case of convex minimization problems, we derive convergence rates for the sequence of objective function values by making use of conjugate duality techniques. Secondly, we propose for the general monotone inclusion problem two new schemes which accelerate the sequences of primal and/or dual iterates, provided strong monotonicity assumptions for some of the involved operators are fulfilled. Finally, we apply the theoretical achievements in the context of different types of image restoration problems solved via total variation regularization.