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An approximate lower order penalty approach for solving second-order cone linear complementarity problems

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Listed:
  • Zijun Hao

    (North Minzu University)

  • Chieu Thanh Nguyen

    (National Taiwan Normal University)

  • Jein-Shan Chen

    (National Taiwan Normal University)

Abstract

Based on a class of smoothing approximations to projection function onto second-order cone, an approximate lower order penalty approach for solving second-order cone linear complementarity problems (SOCLCPs) is proposed, and four kinds of specific smoothing approximations are considered. In light of this approach, the SOCLCP is approximated by asymptotic lower order penalty equations with penalty parameter and smoothing parameter. When the penalty parameter tends to positive infinity and the smoothing parameter monotonically decreases to zero, we show that the solution sequence of the asymptotic lower order penalty equations converges to the solution of the SOCLCP at an exponential rate under a mild assumption. A corresponding algorithm is constructed and numerical results are reported to illustrate the feasibility of this approach. The performance profile of four specific smoothing approximations is presented, and the generalization of two approximations are also investigated.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jglopt:v:83:y:2022:i:4:d:10.1007_s10898-021-01116-w
    DOI: 10.1007/s10898-021-01116-w
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    References listed on IDEAS

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    1. Jein-Shan Chen, 2019. "SOC Functions and Their Applications," Springer Optimization and Its Applications, Springer, number 978-981-13-4077-2, June.
    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. C. E. Lemke, 1965. "Bimatrix Equilibrium Points and Mathematical Programming," Management Science, INFORMS, vol. 11(7), pages 681-689, May.
    4. M. Seetharama Gowda & Jong-Shi Pang, 1992. "On Solution Stability of the Linear Complementarity Problem," Mathematics of Operations Research, INFORMS, vol. 17(1), pages 77-83, February.
    5. 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.
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