IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v180y2019i2d10.1007_s10957-018-1364-8.html
   My bibliography  Save this article

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

Author

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
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10957-018-1364-8
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10957-018-1364-8?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. M. Soledad Aronna & J. Frédéric Bonnans & Pierre Martinon, 2013. "A Shooting Algorithm for Optimal Control Problems with Singular Arcs," Journal of Optimization Theory and Applications, Springer, vol. 158(2), pages 419-459, August.
    2. Cao, Yankai & Zavala, Victor M. & D’Amato, Fernando, 2018. "Using stochastic programming and statistical extrapolation to mitigate long-term extreme loads in wind turbines," Applied Energy, Elsevier, vol. 230(C), pages 1230-1241.
    3. Bethany L. Nicholson & Wei Wan & Shivakumar Kameswaran & Lorenz T. Biegler, 2018. "Parallel cyclic reduction strategies for linear systems that arise in dynamic optimization problems," Computational Optimization and Applications, Springer, vol. 70(2), pages 321-350, June.
    4. Huster, Wolfgang R. & Vaupel, Yannic & Mhamdi, Adel & Mitsos, Alexander, 2018. "Validated dynamic model of an organic Rankine cycle (ORC) for waste heat recovery in a diesel truck," Energy, Elsevier, vol. 151(C), pages 647-661.
    5. Zebian, Hussam & Mitsos, Alexander, 2012. "A double-pinch criterion for regenerative Rankine cycles," Energy, Elsevier, vol. 40(1), pages 258-270.
    6. D. Gerard & M. Köppe & Q. Louveaux, 2017. "Guided dive for the spatial branch-and-bound," Journal of Global Optimization, Springer, vol. 68(4), pages 685-711, August.
    7. Seung-Jun Shin & Duck Bong Kim & Guodong Shao & Alexander Brodsky & David Lechevalier, 2017. "Developing a decision support system for improving sustainability performance of manufacturing processes," Journal of Intelligent Manufacturing, Springer, vol. 28(6), pages 1421-1440, August.
    8. C. Zhang & Q. J. Wei, 2009. "Global and Finite Convergence of a Generalized Newton Method for Absolute Value Equations," Journal of Optimization Theory and Applications, Springer, vol. 143(2), pages 391-403, November.
    9. Brage Rugstad Knudsen & Hanne Kauko & Trond Andresen, 2019. "An Optimal-Control Scheme for Coordinated Surplus-Heat Exchange in Industry Clusters," Energies, MDPI, vol. 12(10), pages 1-22, May.
    10. Aydogmus, Ozgur & TOR, Ali Hakan, 2021. "A Modified Multiple Shooting Algorithm for Parameter Estimation in ODEs Using Adjoint Sensitivity Analysis," Applied Mathematics and Computation, Elsevier, vol. 390(C).
    11. Zhengyong Zhou & Yunchan Peng, 2019. "The locally Chen–Harker–Kanzow–Smale smoothing functions for mixed complementarity problems," Journal of Global Optimization, Springer, vol. 74(1), pages 169-193, May.
    12. E. Trélat, 2012. "Optimal Control and Applications to Aerospace: Some Results and Challenges," Journal of Optimization Theory and Applications, Springer, vol. 154(3), pages 713-758, September.
    13. Yiyin Cao & Yin Chen & Chuangyin Dang, 2024. "A Variant of the Logistic Quantal Response Equilibrium to Select a Perfect Equilibrium," Journal of Optimization Theory and Applications, Springer, vol. 201(3), pages 1026-1062, June.
    14. M. Gerdts, 2006. "Local Minimum Principle for Optimal Control Problems Subject to Differential-Algebraic Equations of Index Two," Journal of Optimization Theory and Applications, Springer, vol. 130(3), pages 443-462, September.
    15. Lizarraga-Garcia, Enrique & Ghobeity, Amin & Totten, Mark & Mitsos, Alexander, 2013. "Optimal operation of a solar-thermal power plant with energy storage and electricity buy-back from grid," Energy, Elsevier, vol. 51(C), pages 61-70.
    16. Pin-Bo Chen & Gui-Hua Lin & Xide Zhu & Fusheng Bai, 2021. "Smoothing Newton method for nonsmooth second-order cone complementarity problems with application to electric power markets," Journal of Global Optimization, Springer, vol. 80(3), pages 635-659, July.
    17. Gerdts, Matthias, 2008. "A nonsmooth Newton’s method for control-state constrained optimal control problems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(4), pages 925-936.
    18. Louis Caccetta & Biao Qu & Guanglu Zhou, 2011. "A globally and quadratically convergent method for absolute value equations," Computational Optimization and Applications, Springer, vol. 48(1), pages 45-58, January.
    19. Nina Ovcharova & Joachim Gwinner, 2014. "A Study of Regularization Techniques of Nondifferentiable Optimization in View of Application to Hemivariational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 162(3), pages 754-778, September.
    20. Dizqah, Arash M. & Maheri, Alireza & Busawon, Krishna, 2014. "An accurate method for the PV model identification based on a genetic algorithm and the interior-point method," Renewable Energy, Elsevier, vol. 72(C), pages 212-222.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:joptap:v:180:y:2019:i:2:d:10.1007_s10957-018-1364-8. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.