IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v10y2022i5p691-d756465.html
   My bibliography  Save this article

Optimal Control Problems for Set-Valued Quasivariational Inequalities with Applications

Author

Listed:
  • Shih-Sen Chang

    (Center for General Education, China Medical University, Taichung 40402, Taiwan)

  • Salahuddin

    (Department of Mathematics, Jazan University, Jazan 45142, Saudi Arabia)

  • Lin Wang

    (College of Statistics and Mathematics, Yunnan University of Fiance and Ecoomics, Kunming 650221, China)

  • Jinfang Tang

    (Department of mathematics, Yibin University, Yibin 644007, China)

  • Liangcai Zhao

    (Department of mathematics, Yibin University, Yibin 644007, China)

Abstract

In this paper we investigate the optimal control problem for set-valued quasivariational inequality with unilateral constraints. Under suitable conditions, we prove that the solution to the current optimal control problem converges to a solution to old control problems. By way of application, we utilize our results presented in the paper to study the optimal control associated with boundary value problems which is described by frictional contact problems and a stationary heat transfer problem with unilateral constraints.

Suggested Citation

  • Shih-Sen Chang & Salahuddin & Lin Wang & Jinfang Tang & Liangcai Zhao, 2022. "Optimal Control Problems for Set-Valued Quasivariational Inequalities with Applications," Mathematics, MDPI, vol. 10(5), pages 1-19, February.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:5:p:691-:d:756465
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/10/5/691/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/10/5/691/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Mahdi Boukrouche & Domingo Tarzia, 2012. "Convergence of distributed optimal control problems governed by elliptic variational inequalities," Computational Optimization and Applications, Springer, vol. 53(2), pages 375-393, October.
    2. Zijia Peng & Karl Kunisch, 2018. "Optimal Control of Elliptic Variational–Hemivariational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 178(1), pages 1-25, July.
    3. Khalid Addi & Daniel Goeleven, 2017. "Complementarity and Variational Inequalities in Electronics," Springer Optimization and Its Applications, in: Nicholas J. Daras & Themistocles M. Rassias (ed.), Operations Research, Engineering, and Cyber Security, pages 1-43, Springer.
    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. Jinxia Cen & Tahar Haddad & Van Thien Nguyen & Shengda Zeng, 2022. "Simultaneous distributed-boundary optimal control problems driven by nonlinear complementarity systems," Journal of Global Optimization, Springer, vol. 84(3), pages 783-805, November.
    2. Chinedu Izuchukwu & Yekini Shehu & Chibueze C. Okeke, 2023. "Extension of forward-reflected-backward method to non-convex mixed variational inequalities," Journal of Global Optimization, Springer, vol. 86(1), pages 123-140, May.
    3. Samir Adly, 2019. "A Coderivative Approach to the Robust Stability of Composite Parametric Variational Systems: Applications in Nonsmooth Mechanics," Journal of Optimization Theory and Applications, Springer, vol. 180(1), pages 62-90, January.
    4. Samir Adly & Tahar Haddad & Ba Khiet Le, 2019. "State-Dependent Implicit Sweeping Process in the Framework of Quasistatic Evolution Quasi-Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 182(2), pages 473-493, August.
    5. Tong-tong Shang & Guo-ji Tang, 2023. "Mixed polynomial variational inequalities," Journal of Global Optimization, Springer, vol. 86(4), pages 953-988, August.
    6. L. F. Bueno & G. Haeser & F. Lara & F. N. Rojas, 2020. "An Augmented Lagrangian method for quasi-equilibrium problems," Computational Optimization and Applications, Springer, vol. 76(3), pages 737-766, July.
    7. Nicolas Hadjisavvas & Felipe Lara & Dinh The Luc, 2020. "A general asymptotic function with applications in nonconvex optimization," Journal of Global Optimization, Springer, vol. 78(1), pages 49-68, September.
    8. Sorin-Mihai Grad & Felipe Lara, 2021. "Solving Mixed Variational Inequalities Beyond Convexity," Journal of Optimization Theory and Applications, Springer, vol. 190(2), pages 565-580, August.
    9. Felipe Lara & Rubén López & Benar F. Svaiter, 2019. "A Further Study on Asymptotic Functions via Variational Analysis," Journal of Optimization Theory and Applications, Springer, vol. 182(1), pages 366-382, July.
    10. Felipe Lara, 2020. "Optimality Conditions for Nonconvex Nonsmooth Optimization via Global Derivatives," Journal of Optimization Theory and Applications, Springer, vol. 185(1), pages 134-150, April.
    11. Alfredo Iusem & Felipe Lara, 2019. "Existence Results for Noncoercive Mixed Variational Inequalities in Finite Dimensional Spaces," Journal of Optimization Theory and Applications, Springer, vol. 183(1), pages 122-138, October.

    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:gam:jmathe:v:10:y:2022:i:5:p:691-:d:756465. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.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.