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A Class of Delay Differential Variational Inequalities

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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.

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Acknowledgments

The authors would like to thank Professors Franco Giannessi and Joachim Gwinner and the anonymous referees for their patience and valuable comments. In particular, Professor Joachim Gwinner has pointed out several serious deficits in the earlier version of the paper and made some useful suggestions to strengthen some results of the paper. We are deeply indebted to them for their encouragement.

This work was supported by the National Natural Science Foundation of China (11501263, 71463023, 41461025, 71473109, 71363019), MOE Project of Humanities and Social Sciences (14YJCZH114), China Postdoctoral Science Foundation (2014M551854, 2015M570195), the Natural Science Foundation of Jiangxi Province, China(20142BAB211019), the Humanities and Social Sciences Project of Jiangxi Province, China(2015YJ302), the key project of Youth Science Fund of Jiangxi China (20131542040017).

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Authors and Affiliations

  1. School of Information Technology, Jiangxi University of Finance and Economics, Nanchang, China

    Xing Wang & Ya-wei Qi

  2. School of Statistics, Jiangxi University of Finance and Economics, Nanchang, China

    Chang-qi Tao

  3. School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu, China

    Yi-bin Xiao

Authors
  1. Xing Wang
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  2. Ya-wei Qi
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  3. Chang-qi Tao
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  4. Yi-bin Xiao
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Corresponding author

Correspondence to Xing Wang.

Appendix: The Code for Numerical Example

Appendix: The Code for Numerical Example

The algorithm for Example 5.1 was coded as follows:

figure a

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Wang, X., Qi, Yw., Tao, Cq. et al. A Class of Delay Differential Variational Inequalities. J Optim Theory Appl 172, 56–69 (2017). https://doi.org/10.1007/s10957-016-1002-2

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  • DOI: https://doi.org/10.1007/s10957-016-1002-2

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