Levenberg--Marquardt Methods Based on Probabilistic Gradient Models and Inexact Subproblem Solution, with Application to Data Assimilation

DOI10.1137/140974687zbMath1358.90156OpenAlexW2189373477WikidataQ58040481 ScholiaQ58040481MaRDI QIDQ3179313

Serge Gratton, Luis Nunes Vicente, El Houcine Bergou

Publication date: 21 December 2016

Published in: SIAM/ASA Journal on Uncertainty Quantification (Search for Journal in Brave)

Full work available at URL: http://oatao.univ-toulouse.fr/22604/1/bergou_22604.pdf

zbMATH Keywords

regularizationLevenberg-Marquardt methodvariational data assimilationnonlinear least squaresrandom modelsinexactnessensemble Kalman filter/smootherKalman filter/smoother

Mathematics Subject Classification ID

Nonlinear programming (90C30) Derivative-free methods and methods using generalized derivatives (90C56) Stochastic programming (90C15) Least squares and related methods for stochastic control systems (93E24)

Related Items (12)

A Levenberg-Marquardt method for large nonlinear least-squares problems with dynamic accuracy in functions and gradients ⋮ A Stochastic Levenberg--Marquardt Method Using Random Models with Complexity Results ⋮ Scalable subspace methods for derivative-free nonlinear least-squares optimization ⋮ Convergence analysis of a subsampled Levenberg-Marquardt algorithm ⋮ Convergence and complexity analysis of a Levenberg-Marquardt algorithm for inverse problems ⋮ Numerical linear algebra in data assimilation ⋮ On the complexity of a stochastic Levenberg-Marquardt method ⋮ A non-linear conjugate gradient in dual space for \(L_p\)-norm regularized non-linear least squares with application in data assimilation ⋮ A Nonmonotone Matrix-Free Algorithm for Nonlinear Equality-Constrained Least-Squares Problems ⋮ A derivative-free Gauss-Newton method ⋮ A robust adaptive iterative ensemble smoother scheme for practical history matching applications ⋮ Levenberg-Marquardt method based on probabilistic Jacobian models for nonlinear equations

Uses Software

• EnKF

Cites Work

• On the convergence of the ensemble Kalman filter.
• Convergence of Trust-Region Methods Based on Probabilistic Models
• Introduction to Derivative-Free Optimization
• An Algorithm for Least-Squares Estimation of Nonlinear Parameters
• Nonlinear least squares — the Levenberg algorithm revisited
• The Iterated Kalman Smoother as a Gauss–Newton Method
• Trust Region Methods
• A method for the solution of certain non-linear problems in least squares
• Probability
• Data Assimilation
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