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Exact computation of an error bound for the balanced linear complementarity problem with unique solution

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Abstract

This paper considers the balanced form of the standard linear complementarity problem with unique solution and provides a more precise expression of an upper error bound discovered by Chen and Xiang and published in 2006. This expression has at least two advantages. It makes possible the exact computation of the error bound factor and it provides a satisfactory upper estimate of that factor in terms of the data bitlength when the data is formed of rational numbers. Along the way, we show that, when any rowwise convex combination of two square matrices is nonsingular, the \(\ell _\infty \) norm of the inverse of these rowwise convex combinations is maximized by an extreme diagonal matrix.

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Acknowledgements

We would like to thank the referees for their helpful comments and suggestions.

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Authors and Affiliations

  1. Département d’Informatique, Faculté des Sciences, Université de Sherbrooke, Sherbrooke, Canada

    Jean-Pierre Dussault

  2. INRIA Paris, 2 rue Simone Iff, CS 42112, 75589, Paris Cedex 12, France

    Jean Charles Gilbert

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  1. Jean-Pierre Dussault
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  2. Jean Charles Gilbert
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Correspondence to Jean Charles Gilbert.

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This research was partially supported by NSERC grant OGP0005491.

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Dussault, JP., Gilbert, J.C. Exact computation of an error bound for the balanced linear complementarity problem with unique solution. Math. Program. 199, 1221–1238 (2023). https://doi.org/10.1007/s10107-022-01860-1

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