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Linear Model Predictive Control (MPC) is a widely used method to control systems with linear dynamics. Efficient interior-point methods have been proposed which leverage the block diagonal structure of the quadratic program (QP) resulting from the receding horizon control formulation. However, they require two matrix factorizations per interior-point method iteration, one each for the computation of the dual and the primal. Recently though an interior point method based on the null-space method has been proposed which requires only a single decomposition per iteration. While the then used null-space basis leads to dense null-space projections, in this work we propose a sparse null-space basis which preserves the block diagonal structure of the MPC matrices. Since it is based on the inverse of the transfer matrix we introduce the notion of so-called virtual controls which enables just that invertibility. A combination of the reduced number of factorizations and omission of the evaluation of the dual lets our solver outperform others in terms of computational speed by an increasing margin dependent on the number of state and control variables.
Move blocking (MB) is a widely used strategy to reduce the degrees of freedom of the Optimal Control Problem (OCP) arising in receding horizon control. The size of the OCP is reduced by forcing the input variables to be constant over multiple discret
Bi-level optimization model is able to capture a wide range of complex learning tasks with practical interest. Due to the witnessed efficiency in solving bi-level programs, gradient-based methods have gained popularity in the machine learning communi
Total generalization variation (TGV) is a very powerful and important regularization for various inverse problems and computer vision tasks. In this paper, we proposed a semismooth Newton based augmented Lagrangian method to solve this problem. The a
In linear optimization, matrix structure can often be exploited algorithmically. However, beneficial presolving reductions sometimes destroy the special structure of a given problem. In this article, we discuss structure-aware implementations of pres
In this chapter, we present some recent progresses on the numerics for stochastic distributed parameter control systems, based on the emph{finite transposition method} introduced in our previous works. We first explain how to reduce the numerics of s