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Existence and uniqueness of solutions of the generalized polynomial variational inequality

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Abstract

In this paper, we consider the generalized polynomial variational inequality, which is a subclass of generalized variational inequalities; and it covers several classes of variational inequalities with polynomial functions studied recently in the literature. A well-known existence and uniqueness theorem for the generalized variational inequality was established by Pang and Yao (SIAM J Control Optim 33:168–184, 1995). It is not difficult to show that the conditions of this theorem do not hold for generalized variational inequalities with general polynomial functions. In this paper, in terms of properties of the involved polynomial and by making use of the theory related to exceptional family of elements, we establish an existence and uniqueness theorem for the generalized polynomial variational inequality. A specific example is given to confirm our theoretical findings.

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Authors and Affiliations

  1. School of Mathematics, Tianjin University, Tianjin, 300072, People’s Republic of China

    Jing Wang, Zheng-Hai Huang & Yang Xu

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  1. Jing Wang
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  2. Zheng-Hai Huang
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Correspondence to Zheng-Hai Huang.

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This author’s work was supported by the National Natural Science Foundation of China (Grant Nos. 11431002 and 11871051).

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Wang, J., Huang, ZH. & Xu, Y. Existence and uniqueness of solutions of the generalized polynomial variational inequality. Optim Lett 14, 1571–1582 (2020). https://doi.org/10.1007/s11590-019-01461-6

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