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Solution Stability of a Linearly Perturbed Constraint System and Applications

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Abstract

Linear complementarity problems and affine variational inequalities have been intensively investigated by different methods. Recently, some authors have shown that solution stability of these problems with respect to total perturbations can be effectively studied via a generalized linear constraint system. The present paper focuses on characterizing stability properties of the solution map of a linearly perturbed generalized linear constraint system. The obtained results lead to several stability conditions for parametric linear complementarity problems and affine variational inequalities in explicit forms.

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Acknowledgments

This research is funded by China Medical University (Taichung, Taiwan). The first author would like to thank Prof. J.-C. Yao for hospitality during her six-month stay in Taiwan in 2015. Prof. N. D. Yen’s and anonymous referees’ many helpful remarks and suggestions are gratefully acknowledged. In particular, thanks to a detailed guidance of one of the referees, we are able to improve the results of Sections 4 and 5, and put these sections in better forms.

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Authors and Affiliations

  1. Graduate Training Center, Institute of Mathematics, Vietnam Academy of Science and Technology, 18 Hoang Quoc Viet, Hanoi, 10307, Vietnam

    D. T. K. Huyen

  2. Center for General Education, China Medical University, Taichung, 40402, Taiwan

    J.-C. Yao

Authors
  1. D. T. K. Huyen
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  2. J.-C. Yao
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Corresponding author

Correspondence to D. T. K. Huyen.

Additional information

J.-C. Yao was partially supported by the Grant MOST 105-2115-M-039-002-MY3.

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Huyen, D.T.K., Yao, JC. Solution Stability of a Linearly Perturbed Constraint System and Applications. Set-Valued Var. Anal 27, 169–189 (2019). https://doi.org/10.1007/s11228-017-0442-7

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  • DOI: https://doi.org/10.1007/s11228-017-0442-7

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