A primal-dual Newton method for distributed Quadratic Programming

This paper considers the problem of solving Quadratic Programs (QP) arising in the context of distributed optimization and optimal control. A dual decomposition approach is used, where the problem is decomposed and solved in parallel, while the coupling constraints are enforced via manipulating the dual variables. In this paper, the local problems are solved using a primal-dual interior point method and the dual variables are updated using a Newton iteration, providing a fast convergence rate. Linear predictors for the local primal-dual variables and the dual variables are introduced to help the convergence of the algorithm. We observe a fast and consistent practical convergence for the proposed algorithm.