IDEAS home Printed from https://ideas.repec.org/a/spr/mathme/v91y2020i3d10.1007_s00186-019-00693-7.html
   My bibliography  Save this article

Convergence properties of a class of exact penalty methods for semi-infinite optimization problems

Author

Listed:
  • Jiachen Ju

    (Shandong Normal University)

  • Qian Liu

    (Shandong Normal University)

Abstract

In this paper, a new class of unified penalty functions are derived for the semi-infinite optimization problems, which include many penalty functions as special cases. They are proved to be exact in the sense that under Mangasarian–Fromovitz constraint qualification conditions, a local solution of penalty problem is a corresponding local solution of original problem when the penalty parameter is sufficiently large. Furthermore, global convergence properties are shown under some conditions. The paper is concluded with some numerical examples proving the applicability of our methods to PID controller design and linear-phase FIR digital filter design.

Suggested Citation

  • Jiachen Ju & Qian Liu, 2020. "Convergence properties of a class of exact penalty methods for semi-infinite optimization problems," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 91(3), pages 383-403, June.
    • Handle: RePEc:spr:mathme:v:91:y:2020:i:3:d:10.1007_s00186-019-00693-7
    DOI: 10.1007/s00186-019-00693-7
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00186-019-00693-7
    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/s00186-019-00693-7?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. Qian Liu & Changyu Wang & Xinmin Yang, 2013. "On the convergence of a smoothed penalty algorithm for semi-infinite programming," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 78(2), pages 203-220, October.
    2. Changyu Wang & Cheng Ma & Jinchuan Zhou, 2014. "A new class of exact penalty functions and penalty algorithms," Journal of Global Optimization, Springer, vol. 58(1), pages 51-73, January.
    3. C. Ling & L. Q. Qi & G. L. Zhou & S. Y. Wu, 2006. "Global Convergence of a Robust Smoothing SQP Method for Semi-Infinite Programming," Journal of Optimization Theory and Applications, Springer, vol. 129(1), pages 147-164, April.
    4. Dong-Hui Li & Liqun Qi & Judy Tam & Soon-Yi Wu, 2004. "A Smoothing Newton Method for Semi-Infinite Programming," Journal of Global Optimization, Springer, vol. 30(2), pages 169-194, November.
    5. Canghua Jiang & Qun Lin & Changjun Yu & Kok Lay Teo & Guang-Ren Duan, 2012. "An Exact Penalty Method for Free Terminal Time Optimal Control Problem with Continuous Inequality Constraints," Journal of Optimization Theory and Applications, Springer, vol. 154(1), pages 30-53, July.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Thinh, Vo Duc & Chuong, Thai Doan & Le Hoang Anh, Nguyen, 2023. "Formulas of first-ordered and second-ordered generalization differentials for convex robust systems with applications," Applied Mathematics and Computation, Elsevier, vol. 455(C).

    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. V. Dolgopolik, 2018. "A Unified Approach to the Global Exactness of Penalty and Augmented Lagrangian Functions II: Extended Exactness," Journal of Optimization Theory and Applications, Springer, vol. 176(3), pages 745-762, March.
    2. Qian Liu & Changyu Wang & Xinmin Yang, 2013. "On the convergence of a smoothed penalty algorithm for semi-infinite programming," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 78(2), pages 203-220, October.
    3. Ping Jin & Chen Ling & Huifei Shen, 2015. "A smoothing Levenberg–Marquardt algorithm for semi-infinite programming," Computational Optimization and Applications, Springer, vol. 60(3), pages 675-695, April.
    4. Thinh, Vo Duc & Chuong, Thai Doan & Le Hoang Anh, Nguyen, 2023. "Formulas of first-ordered and second-ordered generalization differentials for convex robust systems with applications," Applied Mathematics and Computation, Elsevier, vol. 455(C).
    5. Lei Zhang & Yang Liu & Jianneng Chen & Heng Zhou & Yunsheng Jiang & Junhua Tong & Lianlian Wu, 2023. "Trajectory Synthesis and Optimization Design of an Unmanned Five-Bar Vegetable Factory Packing Machine Based on NSGA-II and Grey Relation Analysis," Agriculture, MDPI, vol. 13(7), pages 1-21, July.
    6. S. Mishra & M. Jaiswal & H. Le Thi, 2012. "Nonsmooth semi-infinite programming problem using Limiting subdifferentials," Journal of Global Optimization, Springer, vol. 53(2), pages 285-296, June.
    7. Xiaojiao Tong & Soon-Yi Wu & Renjun Zhou, 2010. "New approach for the nonlinear programming with transient stability constraints arising from power systems," Computational Optimization and Applications, Springer, vol. 45(3), pages 495-520, April.
    8. Xiaojiao Tong & Liqun Qi & Soon-Yi Wu & Felix Wu, 2012. "A smoothing SQP method for nonlinear programs with stability constraints arising from power systems," Computational Optimization and Applications, Springer, vol. 51(1), pages 175-197, January.
    9. Takayuki Okuno & Masao Fukushima, 2014. "Local reduction based SQP-type method for semi-infinite programs with an infinite number of second-order cone constraints," Journal of Global Optimization, Springer, vol. 60(1), pages 25-48, September.
    10. Bo Wei & William B. Haskell & Sixiang Zhao, 2020. "An inexact primal-dual algorithm for semi-infinite programming," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 91(3), pages 501-544, June.
    11. M. V. Dolgopolik, 2018. "A Unified Approach to the Global Exactness of Penalty and Augmented Lagrangian Functions I: Parametric Exactness," Journal of Optimization Theory and Applications, Springer, vol. 176(3), pages 728-744, March.
    12. Mengwei Xu & Soon-Yi Wu & Jane Ye, 2014. "Solving semi-infinite programs by smoothing projected gradient method," Computational Optimization and Applications, Springer, vol. 59(3), pages 591-616, December.
    13. Chen Ling & Qin Ni & Liqun Qi & Soon-Yi Wu, 2010. "A new smoothing Newton-type algorithm for semi-infinite programming," Journal of Global Optimization, Springer, vol. 47(1), pages 133-159, May.
    14. Xiaojiao Tong & Chen Ling & Soon-Yi Wu & Liqun Qi, 2013. "Semi-infinite programming method for optimal power flow with transient stability and variable clearing time of faults," Journal of Global Optimization, Springer, vol. 55(4), pages 813-830, April.
    15. Li-Ping Pang & Jian Lv & Jin-He Wang, 2016. "Constrained incremental bundle method with partial inexact oracle for nonsmooth convex semi-infinite programming problems," Computational Optimization and Applications, Springer, vol. 64(2), pages 433-465, June.
    16. Eunice Blanchard & Ryan Loxton & Volker Rehbock, 2014. "Optimal control of impulsive switched systems with minimum subsystem durations," Journal of Global Optimization, Springer, vol. 60(4), pages 737-750, December.
    17. Qian Liu & Yuqing Xu & Yang Zhou, 2020. "A class of exact penalty functions and penalty algorithms for nonsmooth constrained optimization problems," Journal of Global Optimization, Springer, vol. 76(4), pages 745-768, April.
    18. Qun Lin & Ryan Loxton & Kok Teo & Yong Wu, 2015. "Optimal control problems with stopping constraints," Journal of Global Optimization, Springer, vol. 63(4), pages 835-861, December.
    19. C. Ling & L. Q. Qi & G. L. Zhou & S. Y. Wu, 2006. "Global Convergence of a Robust Smoothing SQP Method for Semi-Infinite Programming," Journal of Optimization Theory and Applications, Springer, vol. 129(1), pages 147-164, April.
    20. Bo Wei & William B. Haskell & Sixiang Zhao, 2020. "The CoMirror algorithm with random constraint sampling for convex semi-infinite programming," Annals of Operations Research, Springer, vol. 295(2), pages 809-841, December.

    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:mathme:v:91:y:2020:i:3:d:10.1007_s00186-019-00693-7. 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.