A linear complementarity problem with an n by 2n “P”-matrix

1978 ◽  
pp. 120-141 ◽  
Author(s):  
Ikuyo Kaneko
Keyword(s):  
Linear Complementarity Problem ◽  
Complementarity Problem ◽  
Linear Complementarity ◽  
P Matrix

scholarly journals General fixed-point method for solving the linear complementarity problem

2021 ◽  
Vol 6 (11) ◽  
pp. 11904-11920
Author(s):  
Xi-Ming Fang ◽  
Keyword(s):  
Fixed Point ◽  
Linear Complementarity Problem ◽  
Complementarity Problem ◽  
Sufficient Conditions ◽  
Positive Definite Matrix ◽  
Linear Complementarity ◽  
System Matrix ◽  
Fixed Point Equation ◽  
Point Equation ◽  
P Matrix

<abstract><p>In this paper, we consider numerical methods for the linear complementarity problem (LCP). By introducing a positive diagonal parameter matrix, the LCP is transformed into an equivalent fixed-point equation and the equivalence is proved. Based on such equation, the general fixed-point (GFP) method with two cases are proposed and analyzed when the system matrix is a $ P $-matrix. In addition, we provide several concrete sufficient conditions for the proposed method when the system matrix is a symmetric positive definite matrix or an $ H_{+} $-matrix. Meanwhile, we discuss the optimal case for the proposed method. The numerical experiments show that the GFP method is effective and practical.</p></abstract>

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