A Regularized Saddle-Point Algorithm for Networked Optimization with Resource Allocation Constraints

TL;DR

This paper introduces a regularized saddle-point algorithm for convex networked optimization with resource constraints, improving convergence and communication efficiency in distributed settings.

Contribution

It presents a novel distributed saddle-point method that guarantees convergence under specific step-size conditions, accounting for network topology effects.

Findings

Ensures geometric convergence to the regularized optimal value.

Addresses resource constraints in distributed optimization.

Demonstrates effectiveness on a robotic network example.

Abstract

We propose a regularized saddle-point algorithm for convex networked optimization problems with resource allocation constraints. Standard distributed gradient methods suffer from slow convergence and require excessive communication when applied to problems of this type. Our approach offers an alternative way to address these problems, and ensures that each iterative update step satisfies the resource allocation constraints. We derive step-size conditions under which the distributed algorithm converges geometrically to the regularized optimal value, and show how these conditions are affected by the underlying network topology. We illustrate our method on a robotic network application example where a group of mobile agents strive to maintain a moving target in the barycenter of their positions.