Abstract
Global error bounds for the extended vertical linear complementarity problems (EVLCP) of CKV-type matrices and CKV-type B-matrices are given. These new error bounds have advantages over some existing results on some specific numerical examples.
Similar content being viewed by others
Availability of data and materials
Data sharing not applicable to this article as no data were generated or analyzed during the current study.
References
Cottle, R.W., Dantzig, G.B.: A generalization of the linear complementarity problem. J. Comb. Theory. 8(1), 79–90 (1970)
Fujisawa, T., Kuh, E.S.: Piecewise-linear theory of nonlinear networks. SIAM J. Appl. Math. 22, 307–328 (1972)
Gowda, M.S., Sznajder, R.: A generalization of the Nash equilibrium theorem on bimatrix games. Int. J. Game Theory. 25, 1–12 (1996)
Stavroulakis, G.E.: Impact-echo form a unilateral interlayer crack. LCP-BEM modelling and neural identification. Eng. Fract. Mech. 62(2), 165–184 (1999)
Genot, F., Brogliato, B., Brach, R.M., et al.: On LCPs and tangential inpacts in rigid body mechanics with unilateral constraints and dry friction. IFAC Proc. 30(20), 809–816 (1997)
Yong, L.: Linear complementarity problem and multiobjective optimization. Appl. Mech. Mater. 101–102, 236–239 (2011)
Wang, H.H., Zhang, H.B., Li, C.Q.: Global error bounds for the extended vertical LCP of \(B\)-type matrice. Comput. Appl. Math. 40, 1–15 (2021)
Gowda, M.S., Sznajder, R.: The generalized order linear complementarity problem. SIAM J. Matrix Anal. Appl. 15(3), 779–795 (1994)
Zhang, C., Chen, X.J., Xiu, N.: Global error bounds for the extended vertical LCP. Comput. Optim. Appl. 42(3), 335–352 (2009)
Xiu, N.H., Zhang, J.Z.: A characteristic quantity of \(P\)-matrices. Appl. Math. Lett. 15(2), 41–46 (2002)
Mathias, R., Pang, J.S.: Error bounds for the linear complementarity problem with a \(P\)-matrix. Linear Algebra Appl. 132, 123–136 (1990)
Chen, X.J., Xiang, S.H.: Computation of error bounds for \(P\)-matrix linear complementarity problems. Math. Progr. 106(3), 513–525 (2006)
Cvetković, D.L., Cvetković, L., Li, C.Q.: CKV-type matrices with applications. Linear Algebra Appl. 608(1), 158–184 (2021)
Song, X.N., Gao, L.: CKV-type \(B\)-matrices and error bounds for linear complementarity problems. AIMS Math. 6(10), 10846–10860 (2021)
García-Esnaola, M., Peña, J.M.: Error bounds for linear complementarity problems for \(B\)-matrices. Appl. Math. Lett. 22(7), 1071–1075 (2009)
Acknowledgements
The authors are grateful to the referees for constructive comments and suggestions that helped to improve the presentation.
Funding
This research is supported by Guizhou Provincial Science and Technology Projects (20191161), the Natural Science Research Project of Department of Education of Guizhou Province (QJJ2022015, QJJ2022047), the Talent Growth Project of Education Department of Guizhou Province (2018143), and the Research Foundation of Guizhou Minzu University (2019YB08).
Author information
Authors and Affiliations
Contributions
LY: original draft writing, review writing, and editing. FW: conceptualization, supervision, and funding acquisition. All authors read and approved the final manuscript.
Corresponding author
Ethics declarations
Conflict of interest
The authors declare no competing interests.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
About this article
Cite this article
Yan, L., Wang, F. Global error bounds for the extended vertical linear complementarity problems of CKV-type matrices and CKV-type B-matrices. Japan J. Indust. Appl. Math. 41, 129–150 (2024). https://doi.org/10.1007/s13160-023-00591-w
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s13160-023-00591-w