On an adaptive regularization for ill-posed nonlinear systems and its trust-region implementation

DOI10.1007/s10589-015-9806-9zbMath1336.93055arXiv1504.03442OpenAlexW1630821875MaRDI QIDQ276850

Benedetta Morini, Elisa Riccietti, Stefania Bellavia

Publication date: 4 May 2016

Published in: Computational Optimization and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1504.03442

zbMATH Keywords

regularizationill-posed systems of nonlinear equationsnonlinear stepsize controltrust-region methods

Mathematics Subject Classification ID

Nonlinear systems in control theory (93C10) Adaptive control/observation systems (93C40) Discrete-time control/observation systems (93C55) Regularity of solutions in optimal control (49N60) Inverse problems in optimal control (49N45)

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Uses Software

• levmar

Cites Work

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• On the regularity of trust region-cg algorithm: with application to deconvolution problem
• The regularizing Levenberg-Marquardt scheme is of optimal order
• An improved trust region algorithm for nonlinear equations
• Levenberg--Marquardt methods with strong local convergence properties for solving nonlinear equations with convex constraints
• Convergence rate of the trust region method for nonlinear equations under local error bound condition
• Iterative regularization methods for nonlinear ill-posed problems
• Trust-region quadratic methods for nonlinear systems of mixed equalities and inequalities
• Trust-region and other regularisations of linear least-squares problems
• A new trust region method for nonlinear equations
• A unified local convergence analysis of inexact constrained Levenberg-Marquardt methods
• A two-stage method for nonlinear inverse problems
• A modified trust region algorithm for nonlinear equations with new updating rule of trust region radius
• Convergence of a Regularized Euclidean Residual Algorithm for Nonlinear Least-Squares
• A Regularized Gauss–Newton Trust Region Approach to Imaging in Diffuse Optical Tomography
• A regularizing Levenberg - Marquardt scheme, with applications to inverse groundwater filtration problems
• A Constrained Least Squares Regularization Method for Nonlinear III-Posed Problems
• An Algorithm for Least-Squares Estimation of Nonlinear Parameters
• Numerical Optimization
• Computational Methods for Inverse Problems
• Nonlinear stepsize control, trust regions and regularizations for unconstrained optimization
• Strong local convergence properties of adaptive regularized methods for nonlinear least squares
• Convergence and regularity of trust region methods for nonlinear ill-posed inverse problems
• Toward Global Convergence for Strongly Nonlinear Ill-Posed Problems via a Regularizing Multilevel Approach
• A method for the solution of certain non-linear problems in least squares