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 …

Nonlinearsolve. jl: High-performance and robust solvers for systems of nonlinear equations in julia

A Pal, F Holtorf, A Larsson, T Loman, F Schäefer… - arxiv preprint arxiv …, 2024 - arxiv.org
Efficiently solving nonlinear equations underpins numerous scientific and engineering
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

EH Bergou, Y Diouane, V Kungurtsev - Journal of Optimization Theory and …, 2020 - Springer
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 …

On the convergence and worst-case complexity of trust-region and regularization methods for unconstrained optimization

GN Grapiglia, J Yuan, Y Yuan - Mathematical Programming, 2015 - Springer
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 …

Local convergence of the Levenberg–Marquardt method under Hölder metric subregularity

M Ahookhosh, FJ Aragón Artacho, RMT Fleming… - Advances in …, 2019 - Springer
We describe and analyse Levenberg–Marquardt methods for solving systems of nonlinear
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

Q Rebjock, N Boumal - Mathematical Programming, 2024 - Springer
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 …

Local convergence analysis of the Levenberg–Marquardt framework for nonzero-residue nonlinear least-squares problems under an error bound condition

R Behling, DS Gonçalves, SA Santos - Journal of Optimization Theory and …, 2019 - Springer
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 …

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 …

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 …

[HTML][HTML] Fitting nonlinear equations with the levenberg–marquardt method on google earth engine

S Wang, M Xu, X Zhang, Y Wang - Remote Sensing, 2022 - mdpi.com
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 …