A sign-based linear method for horizontal linear complementarity problems

For the horizontal linear complementarity problem, we establish a linear method based on the sign patterns of the solution of the equivalent modulus equation under the assumption of strict complementarity. The new method is equivalent to solving two linear equations, avoiding parameters selection, s...

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Bibliographic Details
Published in:Numerical algorithms Vol. 91; no. 3; pp. 1165 - 1181
Main Authors: Shao, Xin-Hui, Wang, Zhe, Shen, Hai-Long
Format: Journal Article
Language:English
Published: New York Springer US 01.11.2022
Springer Nature B.V
Subjects:
Algebra
Algorithms
Computer Science
Equivalence
Iterative methods
Linear equations
Methods
Numeric Computing
Numerical Analysis
Original Paper
Sparse matrices
Splitting
Theorems
Theory of Computation
Modulus equation
Sign analysis
Horizontal complementarity problem
ISSN:1017-1398, 1572-9265
Online Access:Get full text
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Summary:For the horizontal linear complementarity problem, we establish a linear method based on the sign patterns of the solution of the equivalent modulus equation under the assumption of strict complementarity. The new method is equivalent to solving two linear equations, avoiding parameters selection, so it is more convenient and practical. Numerical examples show that the new method is superior to the previous modulus-based matrix splitting iterative method, two-step modulus-based matrix splitting iterative method and modulus-based nonsmooth Newton’s method in computing efficiency. The new method can be used as a solution scheme to the horizontal complementarity problem of large sparse matrices.
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ISSN:1017-1398
1572-9265
DOI:10.1007/s11075-022-01296-w