A Distributed Line Search for Network Optimization

Dual descent methods are used to solve network optimization problems because descent directions can be computed in a distributed manner using information available either locally or at neighboring nodes. However, choosing a stepsize in the descent direction remains a challenge because its computation requires global information. This work presents an algorithm based on a local version of the Armijo rule that allows for the computation of a stepsize using only local and neighborhood information. We show that when our distributed line search algorithm is applied with a descent direction computed according to the Accelerated Dual Descent method \cite{acc11}, key properties of standard backtracking line search using the Armijo rule are recovered. We use simulations to demonstrate that our algorithm is a practical substitute for its centralized counterpart.