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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, a differential vector variational inequality is introduced and studied in finite-dimensional Euclidean spaces. The existence of a Carathéodory weak solution for the differential vector variational inequality is presented under some suitable conditions. Furthermore, the upper semicontinuity and the lower semicontinuity of the solution sets for the differential variational inequality are established when both the mapping and the constraint set are perturbed by two different parameters.

Suggested Citation

  • Xing Wang & Nan-Jing Huang, 2013. "Differential Vector Variational Inequalities in Finite-Dimensional Spaces," Journal of Optimization Theory and Applications, Springer, vol. 158(1), pages 109-129, July.
    • Handle: RePEc:spr:joptap:v:158:y:2013:i:1:d:10.1007_s10957-012-0164-9
    DOI: 10.1007/s10957-012-0164-9
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    References listed on IDEAS

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    1. S.J. Li & G.Y. Chen & K.L. Teo, 2002. "On the Stability of Generalized Vector Quasivariational Inequality Problems," Journal of Optimization Theory and Applications, Springer, vol. 113(2), pages 283-295, May.
    2. K. Kimura & J. C. Yao, 2008. "Semicontinuity of Solution Mappings of Parametric Generalized Vector Equilibrium Problems," Journal of Optimization Theory and Applications, Springer, vol. 138(3), pages 429-443, September.
    3. Arvind Raghunathan & J. PÉRez-Correa & Eduardo Agosin & Lorenz Biegler, 2006. "Parameter estimation in metabolic flux balance models for batch fermentation—Formulation & Solution using Differential Variational Inequalities (DVIs)," Annals of Operations Research, Springer, vol. 148(1), pages 251-270, November.
    4. 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.
    5. 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.
    6. 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.
    7. L. C. Ceng & S. Schaible & J. C. Yao, 2008. "Existence of Solutions for Generalized Vector Variational-like Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 137(1), pages 121-133, April.
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    Cited by:

    1. 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.
    2. Heng-you Lan, 2019. "On a class of fuzzy parametric variational inequality controlled differential equation problems in finite dimension spaces," Fuzzy Optimization and Decision Making, Springer, vol. 18(3), pages 327-344, September.
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