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Recent advances in trust region algorithms
Y Yuan - Mathematical Programming, 2015 - Springer
Trust region methods are a class of numerical methods for optimization. Unlike line search
type methods where a line search is carried out in each iteration, trust region methods …
type methods where a line search is carried out in each iteration, trust region methods …
Nonlinearsolve. jl: High-performance and robust solvers for systems of nonlinear equations in julia
Efficiently solving nonlinear equations underpins numerous scientific and engineering
disciplines, yet scaling these solutions for complex system models remains a challenge. This …
disciplines, yet scaling these solutions for complex system models remains a challenge. This …
Convergence and complexity analysis of a Levenberg–Marquardt algorithm for inverse problems
Abstract The Levenberg–Marquardt algorithm is one of the most popular algorithms for
finding the solution of nonlinear least squares problems. Across different modified variations …
finding the solution of nonlinear least squares problems. Across different modified variations …
On the convergence and worst-case complexity of trust-region and regularization methods for unconstrained optimization
A nonlinear stepsize control framework for unconstrained optimization was recently
proposed by Toint (Optim Methods Softw 28: 82–95, 2013), providing a unified setting in …
proposed by Toint (Optim Methods Softw 28: 82–95, 2013), providing a unified setting in …
Local convergence of the Levenberg–Marquardt method under Hölder metric subregularity
We describe and analyse Levenberg–Marquardt methods for solving systems of nonlinear
equations. More specifically, we propose an adaptive formula for the Levenberg–Marquardt …
equations. More specifically, we propose an adaptive formula for the Levenberg–Marquardt …
Fast convergence of trust-regions for non-isolated minima via analysis of CG on indefinite matrices
Trust-region methods (TR) can converge quadratically to minima where the Hessian is
positive definite. However, if the minima are not isolated, then the Hessian there cannot be …
positive definite. However, if the minima are not isolated, then the Hessian there cannot be …
Local convergence analysis of the Levenberg–Marquardt framework for nonzero-residue nonlinear least-squares problems under an error bound condition
Abstract The Levenberg–Marquardt method is widely used for solving nonlinear systems of
equations, as well as nonlinear least-squares problems. In this paper, we consider local …
equations, as well as nonlinear least-squares problems. In this paper, we consider local …
A higher-order Levenberg–Marquardt method for nonlinear equations
X Yang - Applied Mathematics and Computation, 2013 - Elsevier
In this paper, we present a high-order Levenberg–Marquardt method for nonlinear
equations. At every iteration, not only a LM step is computed but also two approximate LM …
equations. At every iteration, not only a LM step is computed but also two approximate LM …
Majorization-minimization-based Levenberg–Marquardt method for constrained nonlinear least squares
N Marumo, T Okuno, A Takeda - Computational Optimization and …, 2023 - Springer
Abstract A new Levenberg–Marquardt (LM) method for solving nonlinear least squares
problems with convex constraints is described. Various versions of the LM method have …
problems with convex constraints is described. Various versions of the LM method have …
[HTML][HTML] Fitting nonlinear equations with the levenberg–marquardt method on google earth engine
Google Earth Engine (GEE) has been widely used to process geospatial data in recent
years. Although the current GEE platform includes functions for fitting linear regression …
years. Although the current GEE platform includes functions for fitting linear regression …