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A modulus-based formulation for the vertical linear complementarity problem

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Abstract

We introduce a modulus-based formulation for vertical linear complementarity problems (VLCPs) with an arbitrary number ℓ of matrices. This formulation can be used to set up a variety of modulus-based solution methods, including, for example, the modulus-based matrix splitting methods for VLCPs that we here introduce. In this context, we particularly analyze the methods for problems with ℓ = 2 (providing also sufficient conditions for their global convergence) and we then generalize the formulation of the methods to any ℓ. Finally, some numerical experiments are solved to evaluate the performance of the proposed methods, which we compare with an existing smoothing Newton method for VLCPs.

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Acknowledgements

The author would like to thank the anonymous referees for their helpful comments and remarks.

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  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

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  1. Francesco Mezzadri
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Correspondence to Francesco Mezzadri.

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Mezzadri, F. A modulus-based formulation for the vertical linear complementarity problem. Numer Algor 90, 1547–1568 (2022). https://doi.org/10.1007/s11075-021-01240-4

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