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Parameter regulation and projection enhancement matrix splitting method: efficient solution for H+ -matrix linear complementarity problems
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DOI：10.1186/s13660-026-03486-9.png)
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Abstract
En 中文
The linear complementarity problem (LCP) serves as a crucial mathematical model for characterizing scenarios such as Nash equilibria in game theory, supply and demand balance in economic systems, and dynamic traffic flow distribution. The development of efficient numerical solutions for LCP holds significant theoretical value and practical significance. This paper proposes the modified matrix splitting iteration (MMSI) method, which introduces a double-diagonal parameter matrix and a relaxation factor to construct a novel iteration format. It innovatively integrates a projection operator to improve the algorithm's robustness with respect to the choice of initial point. Theoretical proof shows that when the coefficient matrix M is a positive definite H+space-matrix with positive diagonal elements, the algorithm globally converges to aspaceuniquespacesolution. Numerical experiments fully demonstrate the efficiency and stability of this algorithm.
Keywords:
Linear complementarity problem
Modified matrix splitting method
Projection operator
Convergence
Numerical experiments
Journal
J
IF:
1.8
Papers:
134
Citations:
0
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