Efficient parallel coordinate descent algorithm for convex optimization problems with separable constraints: application to distributed MPC

TL;DR

This paper introduces a simple, parallel coordinate descent algorithm for convex optimization with separable constraints, suitable for distributed MPC in network systems, demonstrating improved performance and stability.

Contribution

The paper presents a novel parallel coordinate descent algorithm with low complexity, proven convergence, and applicability to distributed MPC, enhancing computational efficiency and stability guarantees.

Findings

Algorithm achieves sublinear convergence rate.

Distributed implementation enables local computation for each subsystem.

Numerical tests show better performance than existing methods.

Abstract

In this paper we propose a parallel coordinate descent algorithm for solving smooth convex optimization problems with separable constraints that may arise e.g. in distributed model predictive control (MPC) for linear network systems. Our algorithm is based on block coordinate descent updates in parallel and has a very simple iteration. We prove (sub)linear rate of convergence for the new algorithm under standard assumptions for smooth convex optimization. Further, our algorithm uses local information and thus is suitable for distributed implementations. Moreover, it has low iteration complexity, which makes it appropriate for embedded control. An MPC scheme based on this new parallel algorithm is derived, for which every subsystem in the network can compute feasible and stabilizing control inputs using distributed and cheap computations. For ensuring stability of the MPC scheme, we use a terminal cost formulation derived from a distributed synthesis. Preliminary numerical tests show better performance for our optimization algorithm than other existing methods.