A BFGS trust-region method for nonlinear equations

DOI10.1007/s00607-011-0146-zzbMath1241.65049OpenAlexW1987878867MaRDI QIDQ644875

Gong Lin Yuan, Zeng-xin Wei, Xi-wen Lu

Publication date: 7 November 2011

Published in: Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00607-011-0146-z

zbMATH Keywords

global convergencenumerical resultsquadratic convergencenonlinear equationstrust region methodBroyden-Fletcher-Goldfarb-Sharma (BFGS) update

Mathematics Subject Classification ID

Numerical mathematical programming methods (65K05) Nonconvex programming, global optimization (90C26) Numerical computation of solutions to systems of equations (65H10) Interior-point methods (90C51) Global methods, including homotopy approaches to the numerical solution of nonlinear equations (65H20)

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Uses Software

• minpack

Cites Work

• A trust-region-based BFGS method with line search technique for symmetric nonlinear equations
• BFGS trust-region method for symmetric nonlinear equations
• A new backtracking inexact BFGS method for symmetric nonlinear equations
• A new trust region method for nonlinear equations
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• The Barzilai and Borwein Gradient Method for the Large Scale Unconstrained Minimization Problem
• The “global” convergence of Broyden-like methods with suitable line search
• An Algorithm for Least-Squares Estimation of Nonlinear Parameters
• Testing Unconstrained Optimization Software
• Comparing Algorithms for Solving Sparse Nonlinear Systems of Equations
• An Efficient Implementation of Merrill’s Method for Sparse or Partially Separable Systems of Nonlinear Equations
• A Globally and Superlinearly Convergent Gauss--Newton-Based BFGS Method for Symmetric Nonlinear Equations
• A Characterization of Superlinear Convergence and Its Application to Quasi-Newton Methods
• Numerical Schubert Calculus by the Pieri Homotopy Algorithm
• A method for the solution of certain non-linear problems in least squares
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