Journal of Optimization Theory and Applications

, Volume 180, Issue 2, pp 500–517 | Cite as

Splitting Methods for a Class of Horizontal Linear Complementarity Problems

  • Francesco MezzadriEmail author
  • Emanuele Galligani


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.


Horizontal linear complementarity problem Matrix splitting Projected methods 

Mathematics Subject Classification

65K05 65H10 90C33 



The authors desire to thank the anonymous referee for the valuable comments and remarks.


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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Engineering “Enzo Ferrari”University of Modena and Reggio EmiliaModenaItaly

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