On the linear convergence of the forward-backward splitting algorithm

In this paper, we establish a linear convergence result for the forward-backward splitting algorithm in the finding a zero of the sum of two maximal monotone operators, where one of them is set-valued strongly monotone and the other is Lipschitz continuous. We show that our convergence rate is better than Douglas–Rachford splitting algorithm’s rate used … Read more

Douglas-Rachford method for the feasibility problem involving a circle and a disc

The Douglas-Rachford algorithm is a classical and a successful method for solving the feasibility problems. Here, we provide a region for global convergence of the algorithm for the feasibility problem involving a disc and a circle in the Euclidean space of dimension two. Citation 1. Borwein, J.M., Sims, B.: The Douglas-Rachford algorithm in the absence … Read more

Stochastic Quasi-Fejér Block-Coordinate Fixed Point Iterations with Random Sweeping

This work investigates the properties of stochastic quasi-Fejér monotone sequences in Hilbert spaces and emphasizes their pertinence in the study of the convergence of block-coordinate fixed point methods. The iterative methods under investigation feature random sweeping rules to select the blocks of variables that are activated over the course of the iterations and allow for … Read more

A Parallel Inertial Proximal Optimization Method

The Douglas-Rachford algorithm is a popular iterative method for finding a zero of a sum of two maximal monotone operators defined on a Hilbert space. In this paper, we propose an extension of this algorithm including inertia parameters and develop parallel versions to deal with the case of a sum of an arbitrary number of … Read more