Levenberg-Marquardt method with singular scaling and applications

Numerical mathematical programming methods (65K05) Nonconvex programming, global optimization (90C26) Numerical methods based on nonlinear programming (49M37) Numerical methods for inverse problems for initial value and initial-boundary value problems involving PDEs (65M32) Numerical methods for inverse problems for boundary value problems involving PDEs (65N21) Inverse problems in optimal control (49N45) PDE constrained optimization (numerical aspects) (49M41)

Cites Work

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On an adaptive regularization for ill-posed nonlinear systems and its trust-region implementation
On the regularity of trust region-cg algorithm: with application to deconvolution problem
Levenberg--Marquardt methods with strong local convergence properties for solving nonlinear equations with convex constraints
Computing the CS and the generalized singular value decompositions
Iterative regularization methods for nonlinear ill-posed problems
General solutions for stationary/moving plane heat source problems in manufacturing and tribology
Space-dependent perfusion coefficient estimation in a 2D bioheat transfer problem
On an elliptical trust-region procedure for ill-posed nonlinear least-squares problems
On the quadratic convergence of the Levenberg-Marquardt method without nonsingularity assumption
Convergence and complexity analysis of a Levenberg-Marquardt algorithm for inverse problems
The minimal-norm Gauss-Newton method and some of its regularized variants
On the convergence of a regularizing Levenberg-Marquardt scheme for nonlinear ill-posed problems
Local convergence analysis of the Levenberg-Marquardt framework for nonzero-residue nonlinear least-squares problems under an error bound condition
A regularizing Levenberg - Marquardt scheme, with applications to inverse groundwater filtration problems
A QUANTITATIVE FORMULATION OF SYLVESTER'S LAW OF INERTIA
Deblurring Images
Nonstandard Scaling Matrices for Trust Region Gauss–Newton Methods
An Algorithm for Least-Squares Estimation of Nonlinear Parameters
Some continuity properties of polyhedral multifunctions
Towards a Generalized Singular Value Decomposition
Generalizing the Singular Value Decomposition
Nonlinear least squares — the Levenberg algorithm revisited
A second order finite volume technique for simulating transport in anisotropic media
Uniqueness for the electrostatic inverse boundary value problem with piecewise constant anisotropic conductivities
Convergence Properties of the Inexact Levenberg-Marquardt Method under Local Error Bound Conditions
Determination of thermal conductivity of inhomogeneous orthotropic materials from temperature measurements
An inexact non stationary Tikhonov procedure for large-scale nonlinear ill-posed problems
Discrete Inverse Problems
Iterated Tikhonov regularization with a general penalty term
Convergence and regularity of trust region methods for nonlinear ill-posed inverse problems
Extension of GKB‐FP algorithm to large‐scale general‐form Tikhonov regularization
A method for the solution of certain non-linear problems in least squares

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