The Matrix Splitting Iteration Method for Nonlinear Complementarity Problems Associated with Second-Order Cone

Abstract

For a class of second-order cone nonlinear complementarity problems, abbreviated as SOCNCPs, we establish the modulus-based matrix splitting relaxation iteration methods, which are obtained by reformulating equivalently SOCNCP as an implicit fixed-point equation based on Jordan algebra associated with the second-order cone. The global convergence theorems are given under suitable choices of the involved splitting matrix and parameter matrices. When the splitting matrix is symmetric positive definite, the strategy choice of the parameters is discussed. Numerical experiments have shown that the modulus-based iteration methods are effective for solving SOCNCPs.

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Correspondence to Yifen Ke.

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This research was supported by National Natural Science Foundation of China (Nos. 11901098 and U1839207) and National Key Research and Development Program of China (Nos. 2018YFC1054200 and 2017YFC0601505).

Communicated by Majid Soleimani-damaneh.

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Ke, Y. The Matrix Splitting Iteration Method for Nonlinear Complementarity Problems Associated with Second-Order Cone. Bull. Iran. Math. Soc. 47, 31–53 (2021). https://doi.org/10.1007/s41980-020-00364-y

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Keywords

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

Mathematics Subject Classification

  • 65H10
  • 90C33