"Operator splitting optimization methods and total variation regularized model "
We first introduce some important optimization methods and their connections with finite difference methods. Then we consider a minimization model with total variational regularization discretized by finite element method, which can be reformulated as a saddle-point problem and then be efficiently solved by the primal-dual method. Our emphasis is analyzing the convergence and convergence rates of a more general primal-dual scheme with a combination factor for the discretized model. Furthermore, a prediction-correction scheme based on the general primal-dual scheme is proposed to relax the step size for the discretization in the time direction. Finally, a faster ADMM with an O(1/n^2) convergence rate is proposed for models without strongly convex objective function.
