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Completely Smooth Lower-Order Penalty Approach for Solving Second-Order Cone Mixed Complementarity Problems

Author

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  • Qiong Wu

    (School of Mathematics and Information Science, North Minzu University, Yinchuan 750021, China)

  • Zijun Hao

    (School of Mathematics and Information Science, North Minzu University, Yinchuan 750021, China)

Abstract

In this paper, a completely smooth lower-order penalty method for solving a second-order cone mixed complementarity problem (SOCMCP) is studied. Four distinct types of smoothing functions are taken into account. According to this method, SOCMCP is approximated by asymptotically completely smooth lower-order penalty equations (CSLOPEs), which includes penalty and smoothing parameters. Under mild assumptions, the main results show that as the penalty parameter approaches positive infinity and the smooth parameter monotonically decreases to zero, the solution sequence of asymptotic CSLOPEs converges exponentially to the solution of SOCMCP. An algorithm based on this approach is developed, and numerical experiments demonstrate its feasibility. The performance profile of four specific smooth functions is given. The final results show that the numerical performance of CSLOPEs is better than that of a smooth-like lower-order penalty method.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:5:p:690-:d:1596021
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. Willard I. Zangwill, 1967. "Non-Linear Programming Via Penalty Functions," Management Science, INFORMS, vol. 13(5), pages 344-358, January.
    4. 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.
    5. 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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