An essentially decentralized interior point method for control

TL;DR

This paper introduces a decentralized primal-dual interior point method with superlinear convergence guarantees for non-convex control problems, demonstrating improved efficiency over ADMM in power system applications.

Contribution

It presents a novel decentralized interior point algorithm with convergence guarantees for non-convex problems, outperforming existing methods like ADMM in speed and complexity.

Findings

Method achieves superlinear convergence for non-convex problems.

Outperforms ADMM in computation time and complexity.

Proven effective on power system control example.

Abstract

Distributed and decentralized optimization are key for the control of networked systems. Application examples include distributed model predictive control and 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 an essentially decentralized primal-dual interior point method with convergence guarantees for non-convex problems at a superlinear rate. We show that the proposed method works reliably on a numerical example from power systems. Our results indicate that the proposed method outperforms ADMM in terms of computation time and computational complexity of the subproblems.