A Distributed Line Search for Network Optimization

TL;DR

This paper introduces a distributed line search algorithm based on a local Armijo rule, enabling stepsize computation using only local information, thus facilitating scalable network optimization.

Contribution

It proposes a novel distributed line search method that approximates centralized stepsize selection using local data, improving the practicality of dual descent methods.

Findings

The algorithm effectively computes stepsizes with only local information.

It recovers key properties of standard Armijo backtracking line search.

Simulations show practical performance comparable to centralized methods.

Abstract

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.