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On Lifting Operators and Regularity of Nonsmooth Newton Methods for Optimal Control Problems of Differential Algebraic Equations

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Abstract

This paper focuses on nonsmooth Newton methods of optimal control problems governed by mixed control–state constraints with differential algebraic equations. In contrast to previous results, we analyze lifting operators involved in nonsmooth Newton methods and establish corresponding convergence results. We also give sufficient conditions for regularity of generalized derivatives of systems of nonsmooth operator equations associated with optimal control problems.

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Acknowledgements

JC is financially supported by DOE (Grant No. DE-FG02-02ER15344). HR is financially supported by NSF (Grant No. CHE-1763198) and DOE (Grant No. DE-FG02-02ER15344).

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Authors and Affiliations

  1. Boston University, Boston, MA, 02215, USA

    Jinhai Chen

  2. Princeton University, Princeton, NJ, 08544, USA

    Herschel Rabitz

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  1. Jinhai Chen
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  2. Herschel Rabitz
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Correspondence to Jinhai Chen.

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Communicated by Boris Vexler.

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Chen, J., Rabitz, H. On Lifting Operators and Regularity of Nonsmooth Newton Methods for Optimal Control Problems of Differential Algebraic Equations. J Optim Theory Appl 180, 518–535 (2019). https://doi.org/10.1007/s10957-018-1364-8

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  • DOI: https://doi.org/10.1007/s10957-018-1364-8

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