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On the global minimization of discretized residual functionals of conditionally well-posed inverse problems

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Abstract

We consider a class of conditionally well-posed inverse problems characterized by a Hölder estimate of conditional stability on a convex compact in a Hilbert space. The input data and the operator of the forward problem are available with errors. We investigate the discretized residual functional constructed according to a general scheme of finite dimensional approximation. We prove that each its stationary point that is not too far from the finite dimensional approximation of the solution to the original inverse problem, generates an approximation from a small neighborhood of this solution. The diameter of the specified neighborhood is estimated in terms of characteristics of the approximation scheme. This partially removes iterating over local minimizers of the residual functional when implementing the discrete quasi-solution method for solving the inverse problem. The developed theory is illustrated by numerical examples.

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Acknowledgements

The author thanks Sergey Paimerov for his help in conducting numerical experiments.

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  1. Mari State University, Yoshkar-Ola, Russia

    M. Yu. Kokurin

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  1. M. Yu. Kokurin
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The work was supported by RSF (Project 20-11-20085)

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Kokurin, M.Y. On the global minimization of discretized residual functionals of conditionally well-posed inverse problems. J Glob Optim 84, 149–176 (2022). https://doi.org/10.1007/s10898-022-01139-x

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  • DOI: https://doi.org/10.1007/s10898-022-01139-x

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