LAUSR

In this article, we consider a class of decentralized nonsmooth composite optimization problems over undirected graphs. The global optimization problem is to minimize the sum of local objective functions consisting of a Lipschitz-differentiable convex function and two possibly nonsmooth convex functions, one of which contains a bounded linear operator. The goal is to solve the global optimization problem through decentralized computation and communication over a network of agents without a central coordinator. Through using triple proximal splitting operators to deal with the nonsmooth terms, we come up with a novel decentralized algorithm with uncoordinated stepsizes, where the stepsizes with independent upper bounds are also distributed for agents or edges over the communication network. Furthermore, we establish the sublinear convergence rate for the proposed algorithm in terms of the first-order optimality residual in a nonergodic sense. Simulation experiments on a constrained quadratic programming problem and an optimal load-sharing problem are carried out to verify the correctness of the theoretical results.