Asynchronous Distributed Optimization via Dual Decomposition and Block Coordinate Subgradient Methods

In this article, we study the problem of minimizing sum potentially nondifferentiable convex cost functions with partially overlapping dependences in an asynchronous manner, where communication network is not coordinated. We behavior algorithm based on dual decomposition and block coordinate subgradient methods under assumptions weaker than those used literature. At same time, allow different agents to use local stepsizes no global coordination. Sufficient conditions are provided for almost sure convergence solution optimization problem. Under additional assumptions, establish a sublinear rate that, turn, can be strengthened linear if strongly has Lipschitz gradients. also extend available results literature by allowing multiple blocks updated at time nonuniform time-varying probabilities assigned blocks. A numerical example illustrate effectiveness algorithm.