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Scalable Relaxation Two-Sweep Modulus-Based Matrix Splitting Methods for Vertical LCP

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  • Dongmei Yu

    (Liaoning Technical University)

  • Huiling Wei

    (Liaoning Technical University)

  • Cairong Chen

    (Fujian Normal University)

  • Deren Han

    (Beihang University)

Abstract

Based on a new equivalent reformulation, a scalable modulus-based matrix splitting (SMMS) method is proposed to solve the vertical linear complementarity problem (VLCP). By introducing a relaxation parameter and employing the two-sweep technique, we further enhance the scalability of the method, leading to a framework of the scalable relaxation two-sweep modulus-based matrix splitting (SRTMMS) method. To theoretically demonstrate the acceleration of the convergence provided by the SMMS method, we present a comparison theorem for the case of $$s=2$$ s = 2 . Furthermore, we establish the convergence of the SRTMMS method for arbitrary s. Preliminary numerical results indicate promising performance of the SRTMMS method.

Suggested Citation

  • Dongmei Yu & Huiling Wei & Cairong Chen & Deren Han, 2024. "Scalable Relaxation Two-Sweep Modulus-Based Matrix Splitting Methods for Vertical LCP," Journal of Optimization Theory and Applications, Springer, vol. 203(1), pages 714-744, October.
    • Handle: RePEc:spr:joptap:v:203:y:2024:i:1:d:10.1007_s10957-024-02529-9
    DOI: 10.1007/s10957-024-02529-9
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    References listed on IDEAS

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    1. Dai, Ping-Fan & Li, Jicheng & Bai, Jianchao & Qiu, Jinming, 2019. "A preconditioned two-step modulus-based matrix splitting iteration method for linear complementarity problem," Applied Mathematics and Computation, Elsevier, vol. 348(C), pages 542-551.
    2. Xia, Zechen & Li, Chenliang, 2015. "Modulus-based matrix splitting iteration methods for a class of nonlinear complementarity problem," Applied Mathematics and Computation, Elsevier, vol. 271(C), pages 34-42.
    3. Nagae, Takeshi & Akamatsu, Takashi, 2008. "A generalized complementarity approach to solving real option problems," Journal of Economic Dynamics and Control, Elsevier, vol. 32(6), pages 1754-1779, June.
    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.
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