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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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Listed:
  • Jinhai Chen

    (Boston University)

  • Herschel Rabitz

    (Princeton University)

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.

Suggested Citation

  • Jinhai Chen & Herschel Rabitz, 2019. "On Lifting Operators and Regularity of Nonsmooth Newton Methods for Optimal Control Problems of Differential Algebraic Equations," Journal of Optimization Theory and Applications, Springer, vol. 180(2), pages 518-535, February.
    • Handle: RePEc:spr:joptap:v:180:y:2019:i:2:d:10.1007_s10957-018-1364-8
    DOI: 10.1007/s10957-018-1364-8
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    References listed on IDEAS

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    1. M. Gerdts, 2003. "Direct Shooting Method for the Numerical Solution of Higher-Index DAE Optimal Control Problems," Journal of Optimization Theory and Applications, Springer, vol. 117(2), pages 267-294, May.
    2. Matthias Gerdts & Martin Kunkel, 2011. "A globally convergent semi-smooth Newton method for control-state constrained DAE optimal control problems," Computational Optimization and Applications, Springer, vol. 48(3), pages 601-633, April.
    3. Eligius M. T. Hendrix & Boglárka G.-Tóth, 2010. "Nonlinear Programming algorithms," Springer Optimization and Its Applications, in: Introduction to Nonlinear and Global Optimization, chapter 5, pages 91-136, Springer.
    4. L. Qi & D. Sun, 2002. "Smoothing Functions and Smoothing Newton Method for Complementarity and Variational Inequality Problems," Journal of Optimization Theory and Applications, Springer, vol. 113(1), pages 121-147, April.
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