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The modulus-based matrix splitting iteration methods for second-order cone linear complementarity problems

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Abstract

For the second-order cone linear complementarity problems, abbreviated as SOCLCPs, we establish two classes of modulus-based matrix splitting iteration methods, which are obtained by reformulating equivalently the SOCLCP as an implicit fixed-point equation based on Jordan algebra associated with the second-order cone. The convergence of these modulus-based matrix splitting iteration methods has been established and the optimal iteration parameters of these methods are discussed when the splitting matrix is symmetric positive definite. Numerical experiments have shown that the modulus-based iteration methods are effective for solving the SOCLCPs.

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Acknowledgments

The authors would like to express their great thankfulness to the referees for the comments and constructive suggestions, which are valuable in improving the quality of the original paper.

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Authors and Affiliations

  1. Key Laboratory of Computational Geodynamics, University of Chinese Academy of Sciences, Beijing, 100049, People’s Republic of China

    Yi-Fen Ke & Huai Zhang

  2. College of Mathematics and Informatics and FJKLMAA, Fujian Normal University, Fuzhou, 350117, People’s Republic of China

    Yi-Fen Ke & Chang-Feng Ma

Authors
  1. Yi-Fen Ke
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  2. Chang-Feng Ma
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  3. Huai Zhang
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Corresponding author

Correspondence to Chang-Feng Ma.

Additional information

This work is supported by China Postdoctoral Science Foundation (No.2017M620878), National Postdoctoral Program for Innovative Talents (No. BX201700234), Fujian Natural Science Foundation (No. 2016J01005), National Basic Research Program of China (No. 2014CB845906), and National Science Foundation of China (No. 41725017, 41590864). It is also partially supported by the Strategic Priority Research Program (B) of the Chinese Academy of Sciences (No. XDB18010202), and the CAS/CAFEA international partnership Program for creative research teams (No. KZZD-EW-TZ-19).

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Ke, YF., Ma, CF. & Zhang, H. The modulus-based matrix splitting iteration methods for second-order cone linear complementarity problems. Numer Algor 79, 1283–1303 (2018). https://doi.org/10.1007/s11075-018-0484-4

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  • DOI: https://doi.org/10.1007/s11075-018-0484-4

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