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Abstract
This work deals with a saddle point formulation of parameter identification in linear elastic contact problems with friction. Using the primal–dual formulation of the constrained minimization problem and given observations, we estimate the Lamé coefficients through the penalization and dualization of the considered inverse problem. By Fenchel duality, we provide the dual energy function associated with the constraint. We prove the existence of a solution to the regularized parameter identification problem as well as the convergence of the penalized problem to the original one. An augmented Lagrangian formulation of the inverse problem and the existence of its saddle point are provided. By means of the alternating direction method of multipliers (ADMM) and a primal–dual active set strategy (PDAS), we solve the problem numerically and illustrate our approach.
Acknowledgments
The authors of this paper express their heartfelt gratitude to the Editorial Office, Editor-in-Chief, Associate Editors, and anonymous reviewers for their valuable and constructive comments and remarks. Their insightful feedback greatly contributed to enhancing the quality and clarity of this work.
Data availability
Data sharing not applicable to this article as no datasets were generated or analysed during the current study.
Disclosure statement
No potential conflict of interest was reported by the author(s).
Financial interests
Authors declare they have no financial interests.