Name
Title | ||
|---|---|---|
Levenberg-Marquardt Methods Based on Probabilistic Gradient Models and Inexact Subproblem Solution, with Application to Data Assimilation |
Abstract | ||
|---|---|---|
The Levenberg-Marquardt algorithm is one of the most popular algorithms for the solution of non-linear 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 algorithm converges globally to a first order stationary point with probability one. Our proposed approach is first tested on simple problems where the exact gradient is perturbed with a Gaussian noise or only called with a certain probability. It is then applied to an instance in variational data assimilation where stochastic models of the gradient are computed by the so-called ensemble methods. |
Year | DOI | Venue |
|---|---|---|
2016 | 10.1137/140974687 | SIAM-ASA JOURNAL ON UNCERTAINTY QUANTIFICATION |
Keywords | Field | DocType |
Levenberg-Marquardt method,nonlinear least squares,regularization,random models,inexactness,variational data assimilation,Kalman filter/smoother,ensemble Kalman filter/smoother | Least squares,Applied mathematics,Mathematical optimization,Stationary point,Probabilistic logic,Non-linear least squares,Ensemble Kalman filter,Ensemble learning,Gaussian noise,Mathematics,Levenberg–Marquardt algorithm | Journal |
Volume | Issue | ISSN |
4 | 1 | 2166-2525 |
Citations | PageRank | References |
3 | 0.42 | 3 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| El Houcine Bergou | 1 | 10 | 3.98 |
| S. Gratton | 2 | 3 | 0.42 |
| luis n vicente | 3 | 176 | 11.24 |