On decentralized convex optimization in a multi-agent setting with separable constraints and its application to optimal charging of electric vehicles

We develop a decentralized algorithm for multiagent, 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 construct a variant of the so called Jacobi algorithm and show that, when the objective function is quadratic, convergence to some minimizer of the centralized problem counterpart is achieved. Our algorithm serves then as an effective alternative to gradient based methodologies. We illustrate its efficacy 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