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Smoothing penalty approach for solving second-order cone complementarity problems

Author

Listed:
  • Chieu Thanh Nguyen

    (Vietnam National University of Agriculture)

  • Jan Harold Alcantara

    (Center for Advanced Intelligence Project, RIKEN)

  • Zijun Hao

    (North Minzu University)

  • Jein-Shan Chen

    (National Taiwan Normal University)

Abstract

In this paper, we propose a smoothing penalty approach for solving the second-order cone complementarity problem (SOCCP). The SOCCP is approximated by a smooth nonlinear equation with penalization parameter. We show that any solution sequence of the approximating equations converges to the solution of the SOCCP under the assumption that the associated function of the SOCCP satisfies a uniform Cartesian-type property. We present a corresponding algorithm for solving the SOCCP based on this smoothing penalty approach, and we demonstrate the efficiency of our method for solving linear, nonlinear and tensor complementarity problems in the second-order cone setting.

Suggested Citation

  • Chieu Thanh Nguyen & Jan Harold Alcantara & Zijun Hao & Jein-Shan Chen, 2025. "Smoothing penalty approach for solving second-order cone complementarity problems," Journal of Global Optimization, Springer, vol. 91(1), pages 39-58, January.
    • Handle: RePEc:spr:jglopt:v:91:y:2025:i:1:d:10.1007_s10898-024-01427-8
    DOI: 10.1007/s10898-024-01427-8
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    References listed on IDEAS

    as
    1. Jein-Shan Chen, 2019. "SOC Functions and Their Applications," Springer Optimization and Its Applications, Springer, number 978-981-13-4077-2, July.
    2. Jein-Shan Chen, 2006. "Two classes of merit functions for the second-order cone complementarity problem," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 64(3), pages 495-519, December.
    3. Zheng-Hai Huang & Tie Ni, 2010. "Smoothing algorithms for complementarity problems over symmetric cones," Computational Optimization and Applications, Springer, vol. 45(3), pages 557-579, April.
    4. Zijun Hao & Chieu Thanh Nguyen & Jein-Shan Chen, 2022. "An approximate lower order penalty approach for solving second-order cone linear complementarity problems," Journal of Global Optimization, Springer, vol. 83(4), pages 671-697, August.
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    Cited by:

    1. Qiong Wu & Zijun Hao, 2025. "Completely Smooth Lower-Order Penalty Approach for Solving Second-Order Cone Mixed Complementarity Problems," Mathematics, MDPI, vol. 13(5), pages 1-20, February.

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