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An improved dual Newton strategy for scenario-tree MPC

This paper considers the problem of solving Quadratic Programs (QPs) in the context of robust Model Predictive Control (MPC) based on scenario trees. A Newton strategy is used in conjunction with dual decomposition, yielding a parallelizable method with a fast practical convergence. In this context, it has been observed that the Hessian of the dual function has an intricate sparsity structure and can be rank deficient, hence requiring a computationally expensive linear algebra and a regularization strategy. In this paper, we show that it is possible to organize the robust MPC problem such that the dual Hessian has a block-tridiagonal structure, hence reducing dramatically the cost of its factorization. Moreover, a simple and inexpensive strategy of constraint elimination is proposed for ensuring the positive definiteness of the dual Hessian, making regularization superfluous. This strategy additionally allows for evening the computational burden of computing the robust MPC solution in its parallelization.