Asynchronous dual descent for separable network optimisation

This study is concerned with the class of convex network optimisation problems forming the Network Utility Maximisation (NUM) framework. Dual decomposition is commonly used to decompose the NUM problem into smaller problems that can be solved locally by the nodes. The typical dual descent techniques suffer however from slow convergence and require the distributed computations to be synchronised. Yet global node synchronisation is a difficult task in self-organised ad-hoc networks, where preference is given to asynchronous protocols. The algorithm proposed in this study proceeds sequentially and asynchronously for each node to local projected gradient descents, combined with local step-size selection routines of the type Armijo. Global convergence is ensured provided that the gradient of the dual function is Lipschitz continuous. Scaling the gradient to the local Newton directions accelerates the process and guarantees linear convergence. The proposed algorithm is tested on the problem of maximum-lifetime routing of a wireless sensor network.