Repository: Freie Universit├Ąt Berlin, Math Department

On the ensemble Kalman inversion under inequality constraints

Hanu, Matei and Weissmann, Simon (2023) On the ensemble Kalman inversion under inequality constraints. arXiv . (Submitted)

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The ensemble Kalman inversion (EKI), a recently introduced optimisation method for solving inverse problems, is widely employed for the efficient and derivative-free estimation of unknown parameters. Specifically in cases involving ill-posed inverse problems and high-dimensional parameter spaces, the scheme has shown promising success. However, in its general form, the EKI does not take constraints into account, which are essential and often stem from physical limitations or specific requirements. Based on a log-barrier approach, we suggest adapting the continuous-time formulation of EKI to incorporate convex inequality constraints. We underpin this adaptation with a theoretical analysis that provides lower and upper bounds on the ensemble collapse, as well as convergence to the constraint optimum for general nonlinear forward models. Finally, we showcase our results through two examples involving partial differential equations (PDEs).

Item Type:Article
Subjects:Mathematical and Computer Sciences > Mathematics > Applied Mathematics
ID Code:3109
Deposited By: Ulrike Eickers
Deposited On:20 Feb 2024 05:40
Last Modified:20 Feb 2024 05:40

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