The main idea in this paper is to implement a distributed primal-dual interior-point algorithm for loosely coupled Quadratic Programming problems. We implement this in Julia and show how can we exploit parallelism in order to increase the computational speed. We investigate the performance of the algorithm on a Model Predictive Control problem.

In this paper we show that chordal structure can be used to devise efficient optimization methods for robust model predictive control problems. To this end, first the problem is converted to an equivalent robust quadratic programming formulation. We then illustrate how the chordal structure can be used to distribute the computations in a primal-dual interior-point method among computational agents, which in turn allows us to accelerate the algorithm by efficient parallel computations. We investigate performance of the framework in Julia using numerical examples.

In this paper, we propose a distributed algorithm for sensor network localization based on a maximum likelihood formulation. It relies on the Levenberg-Marquardt algorithm where the computations are distributed among different computational agents using message passing, or equivalently dynamic programming. The resulting algorithm provides a good localization accuracy, and it converges to the same solution as its centralized counterpart. Moreover, it requires fewer iterations and communications between computational agents as compared to first-order methods. The performance of the algorithm is demonstrated with extensive simulations in Julia in which it is shown that our method outperforms distributed methods that are based on approximate maximum likelihood formulations.

In this paper we present a distributed second-order augmented Lagrangian method for distributed model predictive control. We distribute the computations for search direction, step size, and termination criteria over what is known as the clique tree of the problem and calculate each of them using message passing. The algorithm converges to its centralized counterpart and it requires fewer communications between sub-systems as compared to algorithms such as the alternating direction method of multipliers. Results from a simulation study confirm the efficiency of the framework. Copyright (C) 2021 The Authors.

In this paper, we propose a distributed second-order augmented Lagrangian method for distributed optimal control problems, which can be exploited for distributed model predictive control. We employ a primal-dual interior-point approach for the inner iteration of the augmented Lagrangian and distribute the corresponding computations using message passing over what is known as the clique tree of the problem. The algorithm converges to its centralized counterpart and it requires fewer communications between sub-systems as compared to algorithms such as the alternating direction method of multipliers. We illustrate the efficiency of the framework when applied to randomly generated interconnected sub-systems as well as to a vehicle platooning problem.