Levenberg-Marquardt methods based on probabilistic gradient models and inexact subproblem solution , with application to data assimilation

@inproceedings{Bergou2014LevenbergMarquardtMB,
  title={Levenberg-Marquardt methods based on probabilistic gradient models and inexact subproblem solution , with application to data assimilation},
  author={El Houcine Bergou and Serge Gratton and Lu{\'i}s Nunes Vicente},
  year={2014}
}
The Levenberg-Marquardt algorithm is one of the most popular algorithms for the solution of nonlinear least squares problems. Motivated by the problem structure in data assimilation, we consider in this paper the extension of the classical Levenberg-Marquardt algorithm to the scenarios where the linearized least squares subproblems are solved inexactly and/or the gradient model is noisy and accurate only within a certain probability. Under appropriate assumptions, we show that the modified… CONTINUE READING

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