Journal of Global Optimization

, Volume 70, Issue 2, pp 401–411 | Cite as

Inverse problems for quasi-variational inequalities

Article

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.

Keywords

Inverse problems Regularization Output least-squares Quasi-variational inequalities 

Mathematics Subject Classification

35R30 49N45 65J20 65J22 65M30 

Notes

Acknowledgements

The authors are grateful to the reviewers for the valuable remarks. Akhtar Khan is supported by National Science Foundation Grant 005613-002 and RIT’s COS FEAD Grant for 2016–2017.

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Authors and Affiliations

  1. 1.Center for Applied and Computational Mathematics, School of Mathematical SciencesRochester Institute of TechnologyRochesterUSA
  2. 2.Département de MathématiquesUniversité de PerpignanPerpignanFrance

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