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A Class of Differential Vector Variational Inequalities in Finite Dimensional Spaces

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Abstract

In this paper, we introduce and study a class of differential vector variational inequalities in finite dimensional Euclidean spaces. We establish a relationship between differential vector variational inequalities and differential scalar variational inequalities. Under various conditions, we obtain the existence and linear growth of solutions to the scalar variational inequalities. In particular we prove existence theorems for Carathéodory weak solutions of the differential vector variational inequalities. Furthermore, we give a convergence result on Euler time-dependent procedure for solving the initial-value differential vector variational inequalities.

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Acknowledgements

The authors are grateful to the editor and the referees for their valuable comments and suggestions. This work was supported by the National Natural Science Foundation of China (11171237) and the Key Program of NSFC (Grant No. 70831005).

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  1. Department of Mathematics, Sichuan University, Chengdu, Sichuan, 610064, P.R. China

    Xing Wang & Nan-jing Huang

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  1. Xing Wang
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  2. Nan-jing Huang
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Correspondence to Nan-jing Huang.

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Wang, X., Huang, Nj. A Class of Differential Vector Variational Inequalities in Finite Dimensional Spaces. J Optim Theory Appl 162, 633–648 (2014). https://doi.org/10.1007/s10957-013-0311-y

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