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Structure Exploitation in an Interior-Point Method for Fully Discretized, State Constrained Optimal Control Problems

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Abstract

We discuss a direct discretization method for state-constrained optimal control problems and an interior-point method, which is used to solve the resulting large-scale and sparse nonlinear optimization problems. The main focus of the paper is on the investigation of an efficient method to solve the occurring linear equations with saddle-point structure. To this end, we exploit the particular structure that arises from the optimal control problem and the discretization scheme and use a tailored linear algebra solver alglin in combination with a re-ordering of the saddle-point matrices. Numerical experiments for a simple optimal control problem show a significant speed-up compared to state-of-the-art sparse LU decomposition methods like MA57 or MUMPS in combination with Ipopt.

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Notes

  1. https://www.bitbucket.org/ebertolazzi/alglin

  2. https://software.intel.com/en-us/mkl

  3. http://www.hsl.rl.ac.uk/catalogue/ma57.html

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Authors and Affiliations

  1. Bundeswehr University Munich, Werner-Heisenberg-Weg 39, 85577, Neubiberg, Germany

    Andreas Huber & Matthias Gerdts

  2. University of Trento, Via Sommarive 9, I-38123, Trento, Italy

    Enrico Bertolazzi

Authors
  1. Andreas Huber
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  2. Matthias Gerdts
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  3. Enrico Bertolazzi
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Corresponding author

Correspondence to Matthias Gerdts.

Additional information

This paper is dedicated to Professor Hans Georg Bock on the occasion of his 70th birthday.

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Huber, A., Gerdts, M. & Bertolazzi, E. Structure Exploitation in an Interior-Point Method for Fully Discretized, State Constrained Optimal Control Problems. Vietnam J. Math. 46, 1089–1113 (2018). https://doi.org/10.1007/s10013-018-0318-7

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  • DOI: https://doi.org/10.1007/s10013-018-0318-7

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