Improved Gauss-Seidel type and Jacobi type methods for linear complementarity problems

Wentai Liu (), Yong Wang () and Zheng-Hai Huang ()
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Wentai Liu: Tianjin University
Yong Wang: Tianjin University
Zheng-Hai Huang: Tianjin University

Computational Optimization and Applications, 2025, vol. 92, issue 2, No 10, 683-708

Abstract: Abstract In this paper, we propose two Gauss-Seidel type methods, i.e., the improved modulus-based Gauss-Seidel method and the improved projected Gauss-Seidel method, to solve linear complementarity problems with Z-matrices, in which the diagonal entries of the system matrices may be non-positive. The monotone convergence of the improved modulus-based Gauss-Seidel method is proved minutely. And by proving the equivalence between the improved projected Gauss-Seidel method and the improved modulus-based Gauss-Seidel method, the same property of the improved projected Gauss-Seidel method is also shown. In addition, we also propose the improved modulus-based Jacobi method and show its monotone convergence. These methods extend the applications of the classical modulus-based matrix splitting methods and the classical projected method for solving linear complementarity problems. Finally, our numerical experiments verify our theoretical results. We also compare the three proposed methods and an existing related method, and the results show the effectiveness of the proposed algorithms.

Keywords: Modulus-based Gauss-Seidel method; Projected Gauss-Seidel method; Z-matrix; Linear complementarity problem; Monotone convergence (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s10589-025-00714-8

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