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arXiv · 1802.05062

Contingent derivatives and regularization for noncoercive inverse problems

Christian Clason·Akhtar A. Khan·Miguel Sama·Christiane Tammer
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Abstract

We study the inverse problem of parameter identification in non-coercive variational problems that commonly appear in applied models. We examine the differentiability of the set-valued parameter-to-solution map by using the first-order and the second-order contingent derivatives. We explore the inverse problem by using the output least-squares and the modified output least-squares objectives. By regularizing the non-coercive variational problem, we obtain a single-valued regularized parameter-to-solution map and investigate its smoothness and boundedness. We also consider optimization problems using the output least-squares and the modified output least-squares objectives for the regularized variational problem. We give a complete convergence analysis showing that for the output least-squares and the modified output least-squares, the regularized minimization problems approximate the original optimization problems suitably. We also provide the first-order and the second-order adjoint method for the computation of the first-order and the second-order derivatives of the output least-squares objective. We provide discrete formulas for the gradient and the Hessian calculation and present numerical results.

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Christian Clason, Akhtar A. Khan, Miguel Sama, Christiane Tammer. 2018-02-14. Contingent derivatives and regularization for noncoercive inverse problems. https://doi.org/10.1080/02331934.2018.1442448

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