Regularized Jacobi Iteration for Decentralized Convex Quadratic Optimization with Separable Constraints

We consider multiagent, convex quadratic 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 provide a fixed-point theoretic analysis showing that the algorithm converges to a minimizer of the centralized problem under more relaxed conditions on the regularization coefficient from those available in the literature, and in particular with respect to scaled projected gradient algorithms. The efficacy of the proposed algorithm is illustrated by applying it to the problem of optimal charging of electric vehicles.