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A Class of Delay Differential Variational Inequalities

Author

Listed:
  • Xing Wang

    (Jiangxi University of Finance and Economics)

  • Ya-wei Qi

    (Jiangxi University of Finance and Economics)

  • Chang-qi Tao

    (Jiangxi University of Finance and Economics)

  • Yi-bin Xiao

    (University of Electronic Science and Technology of China)

Abstract

In the paper, we introduce a class of delay differential variational inequalities consisting of a system of delay differential equations and variational inequalities. The existence conclusion of Carathéodory’s weak solution for delay differential variational equalities is obtained. Furthermore, an algorithm for solving the delay differential variational inequality is shown, and the convergence analysis for the algorithm is given. Finally, a numerical example is given to verify the validity of the algorithm.

Suggested Citation

  • Xing Wang & Ya-wei Qi & Chang-qi Tao & Yi-bin Xiao, 2017. "A Class of Delay Differential Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 172(1), pages 56-69, January.
    • Handle: RePEc:spr:joptap:v:172:y:2017:i:1:d:10.1007_s10957-016-1002-2
    DOI: 10.1007/s10957-016-1002-2
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    References listed on IDEAS

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    1. Tahar Haddad, 2013. "Nonconvex Differential Variational Inequality and State-Dependent Sweeping Process," Journal of Optimization Theory and Applications, Springer, vol. 159(2), pages 386-398, November.
    2. Anna Nagurney & Dong Li, 2015. "A supply chain network game theory model with product differentiation, outsourcing of production and distribution, and quality and price competition," Annals of Operations Research, Springer, vol. 226(1), pages 479-503, March.
    3. Nagurney, Anna, 1989. "Migration equilibrium and variational inequalities," Economics Letters, Elsevier, vol. 31(1), pages 109-112.
    4. Terry L. Friesz, 2007. "Dynamic Competition on Networks: Differential Variational Inequalities, Limited Warfare and Internet Vulnerability," International Series in Operations Research & Management Science, in: Terry L. Friesz (ed.), Network Science, Nonlinear Science and Infrastructure Systems, chapter 0, pages 77-98, Springer.
    5. Terry L. Friesz, 2010. "Differential Variational Inequalities and Differential Nash Games," International Series in Operations Research & Management Science, in: Dynamic Optimization and Differential Games, chapter 0, pages 267-312, Springer.
    6. Nagurney, Anna & Pan, Jie & Zhao, Lan, 1992. "Human migration networks," European Journal of Operational Research, Elsevier, vol. 59(2), pages 262-274, June.
    7. 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.
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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.

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