Toward Decentralized Interior Point Methods for Control.
Alexander Engelmann, Gösta Stomberg, Timm Faulwasser · arXiv (Cornell University) · 2021
Distributed and decentralized optimization are key for the control of network systems -- for example in distributed model predictive control, and in distributed sensing or estimation. Non-linear systems, however, lead to problems with non-convex constraints for which classical decentralized optimization algorithms lack convergence guarantees. Moreover, classical decentralized algorithms usually exhibit only linear convergence. This paper presents a decentralized optimization algorithm based on primal-dual interior point methods, which is based on neighbor-to-neighbor communication. We prove local convergence for non-convex problems at a superlinear rate. We show that the method works reliably on a medium-scale numerical example from power systems. Our results indicate that the proposed method outperforms ADMM in terms of computational complexity.