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A Parallel Quadratic Programming Method for Dynamic Optimization Problems

Janick Frasch (frasch***at***ovgu.de)
Sebastian Sager (sager***at***ovgu.de)
Moritz Diehl (moritz.diehl***at***esat.kuleuven.be)

Abstract: Quadratic programming problems (QPs) that arise from dynamic optimization problems typically exhibit a very particular structure. We address the ubiquitous case where these QPs are strictly convex and propose a dual Newton strategy that exploits the block-bandedness similarly to an interior-point method. Still, the proposed method features warmstarting capabilities of active-set methods. We give details for an efficient implementation, including tailored numerical linear algebra, step size computation, parallelization, and infeasibility handling. We prove convergence of the algorithm for the considered problem class. A numerical study based on the open-source implementation qpDUNES shows that the algorithm outperforms both well-established general purpose QP solvers as well as state-of-the-art tailored control QP solvers significantly on the considered benchmark problems.

Keywords: Optimal Control, Quadratic Programming, Model Predictive Control, Open-Source Software

Category 1: Nonlinear Optimization (Quadratic Programming )

Category 2: Applications -- Science and Engineering (Control Applications )

Citation: submitted to Mathematical Programming Computation, 11/2013

Download: [PDF]

Entry Submitted: 11/12/2013
Entry Accepted: 11/12/2013
Entry Last Modified: 11/29/2013

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