IDEAS home Printed from https://ideas.repec.org/a/spr/jglopt/v86y2023i3d10.1007_s10898-022-01260-x.html
   My bibliography  Save this article

The interpolating element-free Galerkin method for the p-Laplace double obstacle mixed complementarity problem

Author

Listed:
  • Rui Ding

    (Soochow University)

  • Chaoren Ding

    (Soochow University)

  • Quan Shen

    (Soochow University)

Abstract

In this paper, the interpolating element-free Galerkin method is presented for the p-Laplace double obstacle mixed complementarity problem when $$1 2$$ p > 2 . First, a nonlinear power penalty equation is obtained by a power penalty approximation method and the existence and uniqueness of the solution to the power penalty equation are proved when $$1 2$$ p > 2 . The convergence of the power penalty solution to the original problem and the penalty estimates are analyzed. Second, the interpolating element-free Galerkin method is constructed for the nonlinear power penalty equation. The numerical implementation is introduced in detail and the convergence of the interpolating element-free Galerkin method is also given. Error estimates indicate that the convergence order depends on not only the spatial step h and the number of bases functions m in the interpolating element-free Galerkin method, but also the index k in the penalty term, the penalty factor $$\lambda $$ λ and p. For different p, the method that how to choose the optimal k and $$\lambda $$ λ is also given. Numerical examples verify error estimates and illustrate the influence of each parameter on the solution.

Suggested Citation

  • Rui Ding & Chaoren Ding & Quan Shen, 2023. "The interpolating element-free Galerkin method for the p-Laplace double obstacle mixed complementarity problem," Journal of Global Optimization, Springer, vol. 86(3), pages 781-820, July.
    • Handle: RePEc:spr:jglopt:v:86:y:2023:i:3:d:10.1007_s10898-022-01260-x
    DOI: 10.1007/s10898-022-01260-x
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10898-022-01260-x
    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/s10898-022-01260-x?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. S. Wang & X. Q. Yang & K. L. Teo, 2006. "Power Penalty Method for a Linear Complementarity Problem Arising from American Option Valuation," Journal of Optimization Theory and Applications, Springer, vol. 129(2), pages 227-254, May.
    2. Yarui Duan & Song Wang & Yuying Zhou, 2021. "A power penalty approach to a mixed quasilinear elliptic complementarity problem," Journal of Global Optimization, Springer, vol. 81(4), pages 901-918, December.
    3. S. A. Gabriel, 1998. "An NE/SQP Method for the Bounded Nonlinear Complementarity Problem," Journal of Optimization Theory and Applications, Springer, vol. 97(2), pages 493-506, May.
    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. Jose Cruz & Daniel Sevcovic, 2020. "On solutions of a partial integro-differential equation in Bessel potential spaces with applications in option pricing models," Papers 2003.03851, arXiv.org.
    2. Kaiwen Meng & Xiaoqi Yang, 2015. "First- and Second-Order Necessary Conditions Via Exact Penalty Functions," Journal of Optimization Theory and Applications, Springer, vol. 165(3), pages 720-752, June.
    3. Anna Clevenhaus & Matthias Ehrhardt & Michael Günther & Daniel Ševčovič, 2020. "Pricing American Options with a Non-Constant Penalty Parameter," JRFM, MDPI, vol. 13(6), pages 1-7, June.
    4. Wen Li & Song Wang, 2014. "A numerical method for pricing European options with proportional transaction costs," Journal of Global Optimization, Springer, vol. 60(1), pages 59-78, September.
    5. 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.
    6. Boshi Tian & Yaohua Hu & Xiaoqi Yang, 2015. "A box-constrained differentiable penalty method for nonlinear complementarity problems," Journal of Global Optimization, Springer, vol. 62(4), pages 729-747, August.
    7. Attipoe, David Sena & Tambue, Antoine, 2021. "Convergence of the mimetic finite difference and fitted mimetic finite difference method for options pricing," Applied Mathematics and Computation, Elsevier, vol. 401(C).
    8. Zhe Sun & Zhe Liu & Xiaoqi Yang, 2015. "On power penalty methods for linear complementarity problems arising from American option pricing," Journal of Global Optimization, Springer, vol. 63(1), pages 165-180, September.
    9. Lesmana, Donny Citra & Wang, Song, 2015. "Penalty approach to a nonlinear obstacle problem governing American put option valuation under transaction costs," Applied Mathematics and Computation, Elsevier, vol. 251(C), pages 318-330.
    10. W. Li & S. Wang, 2009. "Penalty Approach to the HJB Equation Arising in European Stock Option Pricing with Proportional Transaction Costs," Journal of Optimization Theory and Applications, Springer, vol. 143(2), pages 279-293, November.
    11. Yuan Li & Hai-Shan Han & Dan-Dan Yang, 2014. "A Penalized-Equation-Based Generalized Newton Method for Solving Absolute-Value Linear Complementarity Problems," Journal of Mathematics, Hindawi, vol. 2014, pages 1-10, September.
    12. Shuhua Chang & Xinyu Wang, 2015. "Modelling and Computation in the Valuation of Carbon Derivatives with Stochastic Convenience Yields," PLOS ONE, Public Library of Science, vol. 10(5), pages 1-35, May.
    13. R. S. Burachik & X. Q. Yang & Y. Y. Zhou, 2017. "Existence of Augmented Lagrange Multipliers for Semi-infinite Programming Problems," Journal of Optimization Theory and Applications, Springer, vol. 173(2), pages 471-503, May.
    14. K. Zhang, 2012. "Applying a Power Penalty Method to Numerically Pricing American Bond Options," Journal of Optimization Theory and Applications, Springer, vol. 154(1), pages 278-291, July.
    15. K. Zhang & K. Teo, 2013. "Convergence analysis of power penalty method for American bond option pricing," Journal of Global Optimization, Springer, vol. 56(4), pages 1313-1323, August.
    16. Song-Ping Zhu & Xin-Jiang He & XiaoPing Lu, 2018. "A new integral equation formulation for American put options," Quantitative Finance, Taylor & Francis Journals, vol. 18(3), pages 483-490, March.
    17. Chen, Wen & Wang, Song, 2017. "A power penalty method for a 2D fractional partial differential linear complementarity problem governing two-asset American option pricing," Applied Mathematics and Computation, Elsevier, vol. 305(C), pages 174-187.
    18. Y. Zhou & S. Wang & X. Yang, 2014. "A penalty approximation method for a semilinear parabolic double obstacle problem," Journal of Global Optimization, Springer, vol. 60(3), pages 531-550, November.
    19. Y. J. Liu & L. W. Zhang, 2008. "Convergence of the Augmented Lagrangian Method for Nonlinear Optimization Problems over Second-Order Cones," Journal of Optimization Theory and Applications, Springer, vol. 139(3), pages 557-575, December.
    20. Steven A. Gabriel & Andy S. Kydes & Peter Whitman, 2001. "The National Energy Modeling System: A Large-Scale Energy-Economic Equilibrium Model," Operations Research, INFORMS, vol. 49(1), pages 14-25, February.

    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:jglopt:v:86:y:2023:i:3:d:10.1007_s10898-022-01260-x. 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.