Please use this identifier to cite or link to this item: http://hdl.handle.net/10316/45235
Title: Levenberg--Marquardt Methods Based on Probabilistic Gradient Models and Inexact Subproblem Solution, with Application to Data Assimilation
Authors: Bergou, E. 
Gratton, S. 
Vicente, Luís Nunes 
Issue Date: 2016
Publisher: Society for Industrial and Applied Mathematics (SIAM)
Project: info:eu-repo/grantAgreement/FCT/5876/147205/PT 
Serial title, monograph or event: SIAM/ASA Journal on Uncertainty Quantification
Volume: 4
Issue: 1
Abstract: 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 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.
URI: http://hdl.handle.net/10316/45235
Other Identifiers: 10.1137/140974687
DOI: 10.1137/140974687
Rights: openAccess
Appears in Collections:I&D CMUC - Artigos em Revistas Internacionais

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