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Solving reachability problems by a scalable constrained optimization method

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Abstract

In this paper we consider the problem of finding an evolution of a dynamical system that originates and terminates in given sets of states. However, if such an evolution exists then it is usually not unique. We investigate this problem and find a scalable approach for solving it. In addition, the resulting saddle-point matrix is sparse. We exploit the structure in order to reach an efficient implementation of our method. In computational experiments we compare line search and trust-region methods as well as various methods for Hessian approximation.

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Acknowledgements

We thank anonymous referees for useful comments and valuable suggestions that have led to significant improvement of the manuscript. We thank Ctirad Matonoha for his help with numerical experiments.

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Authors and Affiliations

  1. Institute of Computer Science, The Czech Academy of Sciences, Pod Vodarenskou vezi 271/2, 182 07, Prague, Czech Republic

    Jan Kuřátko & Stefan Ratschan

  2. Faculty of Mathematics and Physics, Charles University in Prague, Ke Karlovu 3, 121 16, Prague, Czech Republic

    Jan Kuřátko

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  1. Jan Kuřátko
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  2. Stefan Ratschan
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Correspondence to Jan Kuřátko.

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This work was supported by the Czech Science Foundation (GACR) Grant No. 15-14484S with institutional support RVO:67985807.

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Kuřátko, J., Ratschan, S. Solving reachability problems by a scalable constrained optimization method. Optim Eng 21, 215–239 (2020). https://doi.org/10.1007/s11081-019-09441-6

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