IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v194y2022i3d10.1007_s10957-022-02049-4.html
   My bibliography  Save this article

Optimality Conditions for Linear-Convex Optimal Control Problems with Mixed Constraints

Author

Listed:
  • Jorge Becerril

    (Instituto Tecnológico y de Estudios Superiores de Monterrey)

  • Cristopher Hermosilla

    (Universidad Técnica Federico Santa María)

Abstract

In this paper, we provide sufficient optimality conditions for convex optimal control problems with mixed constraints. On one hand, the data delimiting the problem we consider is continuous and jointly convex on the state and control variables, but on the other hand, smoothness on the data of the problem, on the candidate to minimizer and/or on the multipliers is not needed. We also show that, under a suitable interior feasibility condition, the optimality conditions are necessary as well and can be written as a Maximum Principle in normal form. The novelty of this last part is that no additional regularity conditions on the mixed constraints, such as the Mangasarian–Fromovitz constraint qualification or the bounded slope condition, are required. A discussion about the regularity of the costate is also provided.

Suggested Citation

  • Jorge Becerril & Cristopher Hermosilla, 2022. "Optimality Conditions for Linear-Convex Optimal Control Problems with Mixed Constraints," Journal of Optimization Theory and Applications, Springer, vol. 194(3), pages 795-820, September.
    • Handle: RePEc:spr:joptap:v:194:y:2022:i:3:d:10.1007_s10957-022-02049-4
    DOI: 10.1007/s10957-022-02049-4
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10957-022-02049-4
    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/s10957-022-02049-4?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. Aram Arutyunov & Dmitry Karamzin, 2020. "A Survey on Regularity Conditions for State-Constrained Optimal Control Problems and the Non-degenerate Maximum Principle," Journal of Optimization Theory and Applications, Springer, vol. 184(3), pages 697-723, March.
    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. Askhat Diveev & Elizaveta Shmalko & Vladimir Serebrenny & Peter Zentay, 2020. "Fundamentals of Synthesized Optimal Control," Mathematics, MDPI, vol. 9(1), pages 1-18, December.
    2. Fernando Lobo Pereira & Nathalie T. Khalil, 2022. "A Maximum Principle for a Time-Optimal Bilevel Sweeping Control Problem," Journal of Optimization Theory and Applications, Springer, vol. 192(3), pages 1022-1051, March.

    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:194:y:2022:i:3:d:10.1007_s10957-022-02049-4. 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.