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Noncoercive Variational–Hemivariational Inequalities: Existence, Approximation by Double Regularization, and Application to Nonmonotone Contact Problems

Author

Listed:
  • Ouayl Chadli

    (Ibn Zohr University)

  • Joachim Gwinner

    (Universität der Bundeswehr München)

  • M. Zuhair Nashed

    (University of Central Florida)

Abstract

We study noncoercive nonlinear variational–hemivariational inequalities that encompass semicoercive nonlinear monotone variational inequalities and pseudomonotone variational inequalities in reflexive Banach spaces, respectively, hemivariational inequalities in function spaces. We present existence and approximation results. Our approach consists in a double regularization: we combine a Browder–Tikhonov regularization with regularization tools of nondifferentiable optimization to smooth the jumps in the hemivariational term. As application, we treat a noncoercive unilateral contact problem in continuum mechanics with nonmonotone friction.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:193:y:2022:i:1:d:10.1007_s10957-022-02006-1
    DOI: 10.1007/s10957-022-02006-1
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    References listed on IDEAS

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    1. A. Lahmdani & O. Chadli & J. C. Yao, 2014. "Existence of Solutions for Noncoercive Hemivariational Inequalities by an Equilibrium Approach Under Pseudomonotone Perturbation," Journal of Optimization Theory and Applications, Springer, vol. 160(1), pages 49-66, January.
    2. O. Chadli & Z. Liu & J. C. Yao, 2007. "Applications of Equilibrium Problems to a Class of Noncoercive Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 132(1), pages 89-110, January.
    3. Nina Ovcharova & Joachim Gwinner, 2016. "Semicoercive Variational Inequalities: From Existence to Numerical Solution of Nonmonotone Contact Problems," Journal of Optimization Theory and Applications, Springer, vol. 171(2), pages 422-439, November.
    4. Minh N. Dao & Joachim Gwinner & Dominikus Noll & Nina Ovcharova, 2016. "Nonconvex bundle method with application to a delamination problem," Computational Optimization and Applications, Springer, vol. 65(1), pages 173-203, September.
    5. Nina Ovcharova & Joachim Gwinner, 2014. "A Study of Regularization Techniques of Nondifferentiable Optimization in View of Application to Hemivariational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 162(3), pages 754-778, September.
    6. 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.
    7. O. Chadli & S. Schaible & J. C. Yao, 2004. "Regularized Equilibrium Problems with Application to Noncoercive Hemivariational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 121(3), pages 571-596, June.
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