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Modulus-based matrix splitting methods for a class of horizontal nonlinear complementarity problems

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Abstract

In this paper, we generalize modulus-based matrix splitting methods to a class of horizontal nonlinear complementarity problems (HNCPs). First, we write the HNCP as an implicit fixed-point equation and we introduce the proposed solution procedures. We then prove the convergence of the methods under some assumptions. We also comment on how the proposed methods and convergence theorems generalize existing results on (standard) linear and nonlinear complementarity problems and on horizontal linear complementarity problems. Finally, numerical experiments are solved to demonstrate the efficiency of the procedures. In this context, the effects of the splitting, of the dimension of the matrices, and of the nonlinear term of the problem are analyzed.

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Notes

  1. Since both A and B are nonsingular in the considered problems, we could also proceed similarly by multiplying both sides by B− 1.

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Acknowledgments

The authors would like to thank the anonymous referees for their helpful comments and suggestions.

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Authors and Affiliations

  1. Department of Engineering “Enzo Ferrari”, University of Modena and Reggio Emilia, via P. Vivarelli 10/1, building 26, I-41125, Modena, Italy

    Francesco Mezzadri & Emanuele Galligani

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  1. Francesco Mezzadri
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  2. Emanuele Galligani
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Correspondence to Francesco Mezzadri.

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Mezzadri, F., Galligani, E. Modulus-based matrix splitting methods for a class of horizontal nonlinear complementarity problems. Numer Algor 87, 667–687 (2021). https://doi.org/10.1007/s11075-020-00983-w

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