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A note on Lipschitzian stability of variational inequalities over perturbed polyhedral convex sets

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Abstract

In the previous paper (Optim lett 6:749–762, 2012), under some technical assumptions, we proved that the solution mapping of variational inequalities over perturbed polyhedral convex sets is not Lipschitz-like around points at which the positively linear dependence of the active vectors defining the constraint set is valid. This note shows that the result holds without such assumptions. In addition, for more deeply understanding the results on the Lipschitz-like stability, some examples have been presented.

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Acknowledgments

The author expresses her sincere thanks to two referees for their helpful comments and suggestions. This research is funded by Vietnam National Foundation for Science and Technology Development (NAFOSTED) under Grant Number 101.01-2014.56.

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  1. Department of Mathematics, Vinh University, Vinh, Nghe An, Vietnam

    Nguyen Thi Quynh Trang

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  1. Nguyen Thi Quynh Trang
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Correspondence to Nguyen Thi Quynh Trang.

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Trang, N.T.Q. A note on Lipschitzian stability of variational inequalities over perturbed polyhedral convex sets. Optim Lett 10, 1221–1231 (2016). https://doi.org/10.1007/s11590-015-0915-2

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  • DOI: https://doi.org/10.1007/s11590-015-0915-2

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