An Efficient Numerical Method for the Symmetric Positive Definite Second-Order Cone Linear Complementarity Problem

2019 ◽  
Vol 79 (3) ◽  
pp. 1608-1629 ◽  
Author(s):  
Xiang Wang ◽  
Xing Li ◽  
Lei-Hong Zhang ◽  
Ren-Cang Li
Keyword(s):  
Numerical Method ◽  
Linear Complementarity Problem ◽  
Complementarity Problem ◽  
Linear Complementarity ◽  
Positive Definite ◽  
Second Order ◽  
Symmetric Positive Definite ◽  
Second Order Cone

scholarly journals Generalized SOR-Like Iteration Method for Linear Complementarity Problem

2020 ◽  
Vol 2020 ◽  
pp. 1-6
Author(s):  
Cui-Xia Li ◽  
Shi-Liang Wu
Keyword(s):  
Fixed Point ◽  
Linear Complementarity Problem ◽  
Iteration Method ◽  
Complementarity Problem ◽  
Numerical Experiments ◽  
Linear Complementarity ◽  
Positive Definite ◽  
Convergence Properties ◽  
Fixed Point Equation ◽  
Point Equation

In this paper, we present a generalized SOR-like iteration method to solve the non-Hermitian positive definite linear complementarity problem (LCP), which is obtained by reformulating equivalently the implicit fixed-point equation of the LCP as a two-by-two block nonlinear equation. The convergence properties of the generalized SOR-like iteration method are discussed under certain conditions. Numerical experiments show that the generalized SOR-like method is efficient, compared with the SOR-like method and the modulus-based SOR method.

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