In this paper, we propose two splitting methods for solving horizontal linear complementarity problems characterized by matrices with positive diagonal elements. The proposed procedures are based on the Jacobi and on the Gauss–Seidel iterations and differ from existing techniques in that they act directly and simultaneously on both matrices of the problem. We prove the convergence of the methods under some assumptions on the diagonal dominance of the matrices of the problem. Several numerical experiments, including large-scale problems of practical interest, demonstrate the capabilities of the proposed methods in various situations.

Splitting Methods for a Class of Horizontal Linear Complementarity Problems / Mezzadri, F.; Galligani, E.. - In: JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS. - ISSN 0022-3239. - 180:2(2019), pp. 500-517. [10.1007/s10957-018-1395-1]

Splitting Methods for a Class of Horizontal Linear Complementarity Problems

Mezzadri F.;Galligani E.
2019

Abstract

In this paper, we propose two splitting methods for solving horizontal linear complementarity problems characterized by matrices with positive diagonal elements. The proposed procedures are based on the Jacobi and on the Gauss–Seidel iterations and differ from existing techniques in that they act directly and simultaneously on both matrices of the problem. We prove the convergence of the methods under some assumptions on the diagonal dominance of the matrices of the problem. Several numerical experiments, including large-scale problems of practical interest, demonstrate the capabilities of the proposed methods in various situations.
2019
180
2
500
517
Splitting Methods for a Class of Horizontal Linear Complementarity Problems / Mezzadri, F.; Galligani, E.. - In: JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS. - ISSN 0022-3239. - 180:2(2019), pp. 500-517. [10.1007/s10957-018-1395-1]
Mezzadri, F.; Galligani, E.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11380/1188534
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