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Inverse problems for quasi-variational inequalities

Author

Listed:
  • Akhtar A. Khan

    (Rochester Institute of Technology)

  • Dumitru Motreanu

    (Université de Perpignan)

Abstract

In this short note, our aim is to investigate the inverse problem of parameter identification in quasi-variational inequalities. We develop an abstract nonsmooth regularization approach that subsumes the total variation regularization and permits the identification of discontinuous parameters. We study the inverse problem in an optimization setting using the output-least squares formulation. We prove the existence of a global minimizer and give convergence results for the considered optimization problem. We also discretize the identification problem for quasi-variational inequalities and provide the convergence analysis for the discrete problem. We give an application to the gradient obstacle problem.

Suggested Citation

  • Akhtar A. Khan & Dumitru Motreanu, 2018. "Inverse problems for quasi-variational inequalities," Journal of Global Optimization, Springer, vol. 70(2), pages 401-411, February.
    • Handle: RePEc:spr:jglopt:v:70:y:2018:i:2:d:10.1007_s10898-017-0597-7
    DOI: 10.1007/s10898-017-0597-7
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    References listed on IDEAS

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    1. Frank Lenzen & Florian Becker & Jan Lellmann & Stefania Petra & Christoph Schnörr, 2013. "A class of quasi-variational inequalities for adaptive image denoising and decomposition," Computational Optimization and Applications, Springer, vol. 54(2), pages 371-398, March.
    2. Ciarcià, Carla & Daniele, Patrizia, 2016. "New existence theorems for quasi-variational inequalities and applications to financial models," European Journal of Operational Research, Elsevier, vol. 251(1), pages 288-299.
    3. Akhtar A. Khan & Dumitru Motreanu, 2015. "Existence Theorems for Elliptic and Evolutionary Variational and Quasi-Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 167(3), pages 1136-1161, December.
    4. Annamaria Barbagallo & Paolo Mauro, 2016. "A General Quasi-variational Problem of Cournot-Nash Type and Its Inverse Formulation," Journal of Optimization Theory and Applications, Springer, vol. 170(2), pages 476-492, August.
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    Cited by:

    1. Dumitru Motreanu & Van Thien Nguyen & Shengda Zeng, 2020. "Existence of Solutions for Implicit Obstacle Problems of Fractional Laplacian Type Involving Set-Valued Operators," Journal of Optimization Theory and Applications, Springer, vol. 187(2), pages 391-407, November.
    2. Shengda Zeng & Dumitru Motreanu & Akhtar A. Khan, 2022. "Evolutionary Quasi-Variational-Hemivariational Inequalities I: Existence and Optimal Control," Journal of Optimization Theory and Applications, Springer, vol. 193(1), pages 950-970, June.

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