Regularized Jacobi iteration for decentralized convex optimization with separable constraints

TL;DR

This paper introduces a regularized Jacobi iteration method for decentralized convex optimization with separable constraints, proving convergence and demonstrating its effectiveness in electric vehicle charging scenarios.

Contribution

It develops a novel regularized Jacobi algorithm for decentralized convex optimization, with convergence guarantees and practical application to EV charging.

Findings

Converges to a centralized problem's minimizer for quadratic objectives.

Proven convergence to optimal solutions in general convex cases.

Effective in large-scale EV charging optimization.

Abstract

We consider multi-agent, convex optimization programs subject to separable constraints, where the constraint function of each agent involves only its local decision vector, while the decision vectors of all agents are coupled via a common objective function. We focus on a regularized variant of the so called Jacobi algorithm for decentralized computation in such problems. We first consider the case where the objective function is quadratic, and provide a fixed-point theoretic analysis showing that the algorithm converges to a minimizer of the centralized problem. Moreover, we quantify the potential benefits of such an iterative scheme by comparing it against a scaled projected gradient algorithm. We then consider the general case and show that all limit points of the proposed iteration are optimal solutions of the centralized problem. The efficacy of the proposed algorithm is illustrated by applying it to the problem of optimal charging of electric vehicles, where, as opposed to earlier approaches, we show convergence to an optimal charging scheme for a finite, possibly large, number of vehicles.