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Solution maps of polynomial variational inequalities

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Abstract

In this paper, we investigate several properties of the solution maps of variational inequalities with polynomial data. First, we prove some facts on the \(R_0\)-property, the local boundedness, and the upper semicontinuity of the solution maps. Second, we establish results on the solution existence and the local upper-Hölder stability under the copositivity condition. Third, when the constraint set is semi-algebraic, we discuss the genericity of the \(R_0\)-property and the finite-valuedness of the solution maps.

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Acknowledgements

The author would like to thank Prof. Nguyen Dong Yen, Dr. Pradeep Kumar Sharma, Dr. Vu Thi Huong, and the first anonymous referee for their corrections. The author is indebted to the third anonymous referee for the insightful comments and valuable suggestions.

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  1. CNRS, LIP6, Sorbonne Université, 75005, Paris, France

    Vu Trung Hieu

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  1. Vu Trung Hieu
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Correspondence to Vu Trung Hieu.

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In memory of my teacher Vu Thi Hai (1968–1991).

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Hieu, V.T. Solution maps of polynomial variational inequalities. J Glob Optim 77, 807–824 (2020). https://doi.org/10.1007/s10898-020-00897-w

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