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A Class of Differential Vector Variational Inequalities in Finite Dimensional Spaces

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  • Xing Wang

    (Sichuan University)

  • Nan-jing Huang

    (Sichuan University)

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.

Suggested Citation

  • Xing Wang & Nan-jing Huang, 2014. "A Class of Differential Vector Variational Inequalities in Finite Dimensional Spaces," Journal of Optimization Theory and Applications, Springer, vol. 162(2), pages 633-648, August.
    • Handle: RePEc:spr:joptap:v:162:y:2014:i:2:d:10.1007_s10957-013-0311-y
    DOI: 10.1007/s10957-013-0311-y
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    References listed on IDEAS

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    1. Heemels, W.P.M.H. & Schumacher, J.M. & Weiland, S., 2000. "Linear complimentarity systems," Other publications TiSEM 6cdf0170-6ea9-4fdc-8cfa-6, Tilburg University, School of Economics and Management.
    2. X.Q. Yang & J.C. Yao, 2002. "Gap Functions and Existence of Solutions to Set-Valued Vector Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 115(2), pages 407-417, November.
    3. M. G. Cojocaru & P. Daniele & A. Nagurney, 2005. "Projected Dynamical Systems and Evolutionary Variational Inequalities via Hilbert Spaces with Applications1," Journal of Optimization Theory and Applications, Springer, vol. 127(3), pages 549-563, December.
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    Cited by:

    1. Xing Wang & Zeng-bao Wu & Yi-bin Xiao & Kok Lay Teo, 2020. "Dynamic variational inequality in fuzzy environments," Fuzzy Optimization and Decision Making, Springer, vol. 19(3), pages 275-296, September.
    2. Savin Treanţă, 2021. "On a Class of Differential Variational Inequalities in Infinite-Dimensional Spaces," Mathematics, MDPI, vol. 9(3), pages 1-10, January.
    3. Jinjie Liu & Xinmin Yang & Shengda Zeng & Yong Zhao, 2022. "Coupled Variational Inequalities: Existence, Stability and Optimal Control," Journal of Optimization Theory and Applications, Springer, vol. 193(1), pages 877-909, June.
    4. Stanisław Migórski & Shengda Zeng, 2018. "A class of differential hemivariational inequalities in Banach spaces," Journal of Global Optimization, Springer, vol. 72(4), pages 761-779, December.
    5. Wang, Xing & Qi, Ya-wei & Tao, Chang-qi & Wu, Qi, 2018. "Existence result for differential variational inequality with relaxing the convexity condition," Applied Mathematics and Computation, Elsevier, vol. 331(C), pages 297-306.

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