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A power penalty approach to a mixed quasilinear elliptic complementarity problem

Author

Listed:
  • Yarui Duan

    (Soochow University)

  • Song Wang

    (Curtin University
    Shenzhen University)

  • Yuying Zhou

    (Soochow University)

Abstract

In this paper, a power penalty approximation method is proposed for solving a mixed quasilinear elliptic complementarity problem. The mixed complementarity problem is first reformulated as a double obstacle quasilinear elliptic variational inequality problem. A nonlinear elliptic partial differential equation is then defined to approximate the resulting variational inequality by using a power penalty approach. The existence and uniqueness of the solution to the partial differential penalty equation are proved. It is shown that, under some mild assumptions, the sequence of solutions to the penalty equations converges to the unique solution of the variational inequality problem as the penalty parameter tends to infinity. The error estimates of the convergence of this penalty approach are also derived. At last, numerical experimental results are presented to show that the power penalty approximation method is efficient and robust.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jglopt:v:81:y:2021:i:4:d:10.1007_s10898-021-01000-7
    DOI: 10.1007/s10898-021-01000-7
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    References listed on IDEAS

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    1. M. Bergounioux, 1997. "Use of Augmented Lagrangian Methods for the Optimal Control of Obstacle Problems," Journal of Optimization Theory and Applications, Springer, vol. 95(1), pages 101-126, October.
    2. 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.
    3. Li, Xiaolin & Dong, Haiyun, 2019. "Analysis of the element-free Galerkin method for Signorini problems," Applied Mathematics and Computation, Elsevier, vol. 346(C), pages 41-56.
    4. Song Wang, 2015. "A penalty approach to a discretized double obstacle problem with derivative constraints," Journal of Global Optimization, Springer, vol. 62(4), pages 775-790, August.
    5. 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.
    6. 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.
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    Cited by:

    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. 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.

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