Abstract-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 QP subproblems are solved locally, while the constraints coupling the different subsystems in the time and space domains are enforced by performing a distributed non-smooth Newton iteration on the dual variables. The iterative linear algebra method Conjugate Gradient (CG) is used to compute the dual Newton step. In this context, it has been observed that the dual Hessian can be singular when a poor initial guess for the dual variables is used, hence leading to a failure of the linear algebra. This paper studies this effect and proposes a constraint relaxation strategy to address the problem. It is both formally and experimentally shown that the relaxation prevents the dual Hessian singularity. Moreover, numerical experiments suggest that the proposed relaxation improves significantly the convergence of the Distributed Dual Newton-CG.

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Summary This paper considers the solution of tree‐structured quadratic programs as they may arise in multistage model predictive control. In this context, sampling the uncertainty on prescribed decision points gives rise to different scenarios that are linked to each other via the so‐called nonanticipativity constraints. Previous work suggests to dualize these constraints and apply Newton's method on the dual problem to achieve a parallelizable scheme. However, it has been observed that the globalization strategy in such an approach can be expensive. To alleviate this problem, we propose to dualize both the nonanticipativity constraints and the dynamics to obtain a computationally cheap globalization. The dual Newton system is then reformulated into small highly structured linear systems that can be solved in parallel to a large extent. The algorithm is complemented by an open‐source software implementation that targets embedded optimal control applications.

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 primaldual 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.

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