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Convergence Results for a Class of Generalized Second-Order Evolutionary Variational–Hemivariational Inequalities

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  • Dong-ling Cai

    (University of Electronic Science and Technology of China)

  • Yi-bin Xiao

    (University of Electronic Science and Technology of China)

Abstract

In this paper, we deal with a class of second-order evolutionary history-dependent variational–hemivariational inequalities with constraint. The unique solvability of the considered second-order evolutionary inequality problem is established via a surjectivity result combined with a fixed point theorem. Moreover, we construct a regularized problem for such second-order evolutionary history-dependent variational–hemivariational inequality and show the convergence of the regularized solutions toward the solution of the original problem under some mild assumptions.

Suggested Citation

  • Dong-ling Cai & Yi-bin Xiao, 2024. "Convergence Results for a Class of Generalized Second-Order Evolutionary Variational–Hemivariational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 201(3), pages 1168-1197, June.
    • Handle: RePEc:spr:joptap:v:201:y:2024:i:3:d:10.1007_s10957-024-02396-4
    DOI: 10.1007/s10957-024-02396-4
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    References listed on IDEAS

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    1. Ouayl Chadli & Joachim Gwinner & M. Zuhair Nashed, 2022. "Noncoercive Variational–Hemivariational Inequalities: Existence, Approximation by Double Regularization, and Application to Nonmonotone Contact Problems," Journal of Optimization Theory and Applications, Springer, vol. 193(1), pages 42-65, June.
    2. Yiran He, 2012. "The Tikhonov Regularization Method for Set-Valued Variational Inequalities," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-10, April.
    3. Ouayl Chadli & Qamrul Hasan Ansari & Jen-Chih Yao, 2016. "Mixed Equilibrium Problems and Anti-periodic Solutions for Nonlinear Evolution Equations," Journal of Optimization Theory and Applications, Springer, vol. 168(2), pages 410-440, February.
    Full references (including those not matched with items on IDEAS)

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    1. Ouayl Chadli & Joachim Gwinner & M. Zuhair Nashed, 2022. "Noncoercive Variational–Hemivariational Inequalities: Existence, Approximation by Double Regularization, and Application to Nonmonotone Contact Problems," Journal of Optimization Theory and Applications, Springer, vol. 193(1), pages 42-65, June.
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