General fixed-point method for solving the linear complementarity problem

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 w...

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Bibliographic Details
Published inAIMS mathematics Vol. 6; no. 11; pp. 11904 - 11920
Main Author Fang, Xi-Ming
Format Journal Article
LanguageEnglish
Published AIMS Press 01.01.2021
Subjects
algorithm
convergence
iterative method
linear complementarity problem
solution
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Summary: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.
ISSN:2473-6988
2473-6988
DOI:10.3934/math.2021691