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

Original Paper
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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.

Keywords

Second-order cone Linear complementarity problem Jordan algebra Matrix splitting Iteration method 

Mathematics Subject Classification (2010)

90C33 65H10 

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Notes

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. 1.Key Laboratory of Computational GeodynamicsUniversity of Chinese Academy of SciencesBeijingPeople’s Republic of China
  2. 2.College of Mathematics and Informatics and FJKLMAAFujian Normal UniversityFuzhouPeople’s Republic of China

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