BFGS trust-region method for symmetric nonlinear equations

DOI10.1016/j.cam.2008.10.062zbMath1168.65026OpenAlexW2065471299MaRDI QIDQ1026429

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

Publication date: 25 June 2009

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cam.2008.10.062

zbMATH Keywords

algorithmglobal convergencenumerical resultsnonconvex programmingnonlinear equationssystems of equationsupdateBroyden-Fletcher-Goldfarb-Shanno (BFGS) trust-region method

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)

Related Items (33)

The Hager–Zhang conjugate gradient algorithm for large-scale nonlinear equations ⋮ A non-monotone pattern search approach for systems of nonlinear equations ⋮ A trust region spectral method for large-scale systems of nonlinear equations ⋮ A new filled function for global minimization and system of nonlinear equations ⋮ Adaptive three-term PRP algorithms without gradient Lipschitz continuity condition for nonconvex functions ⋮ A modified nonmonotone BFGS algorithm for unconstrained optimization ⋮ A trust-region-based BFGS method with line search technique for symmetric nonlinear equations ⋮ Family weak conjugate gradient algorithms and their convergence analysis for nonconvex functions ⋮ Gradient trust region algorithm with limited memory BFGS update for nonsmooth convex minimization ⋮ An approximate gradient-type method for nonlinear symmetric equations with convex constraints ⋮ A BFGS trust-region method for nonlinear equations ⋮ Limited memory BFGS method with backtracking for symmetric nonlinear equations ⋮ An adaptive trust region algorithm for large-residual nonsmooth least squares problems ⋮ A limited memory BFGS method for solving large-scale symmetric nonlinear equations ⋮ A Riemannian nonmonotone spectral method for self-adjoint tangent vector field ⋮ Norm descent conjugate gradient methods for solving symmetric nonlinear equations ⋮ A modified conjugate gradient algorithm with backtracking line search technique for large-scale nonlinear equations ⋮ A quasi-Newton algorithm for large-scale nonlinear equations ⋮ A derivative-free conjugate gradient method and its global convergence for solving symmetric nonlinear equations ⋮ A new modified BFGS method for unconstrained optimization problems ⋮ A BFGS algorithm for solving symmetric nonlinear equations ⋮ A modified three-term PRP conjugate gradient algorithm for optimization models ⋮ A new nonmonotone line-search trust-region approach for nonlinear systems ⋮ A New Method with Descent Property for Symmetric Nonlinear Equations ⋮ A derivative-free \textit{RMIL} conjugate gradient projection method for convex constrained nonlinear monotone equations with applications in compressive sensing ⋮ Limited memory technique using trust regions for nonlinear equations ⋮ A Trust Region Algorithm with Conjugate Gradient Technique for Optimization Problems ⋮ A tensor trust-region model for nonlinear system ⋮ A new trust-region method with line search for solving symmetric nonlinear equations ⋮ A modified HZ conjugate gradient algorithm without gradient Lipschitz continuous condition for non convex functions ⋮ A three-terms Polak-Ribière-Polyak conjugate gradient algorithm for large-scale nonlinear equations ⋮ An active-set projected trust-region algorithm with limited memory BFGS technique for box-constrained nonsmooth equations ⋮ A modified Hestenes and Stiefel conjugate gradient algorithm for large-scale nonsmooth minimizations and nonlinear equations

Uses Software

• GQTPAR

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• The superlinear convergence analysis of a nonmonotone BFGS algorithm on convex objective functions
• A modified PRP conjugate gradient method
• A new backtracking inexact BFGS method for symmetric nonlinear equations
• Testing parallel variable transformation
• On the truncated conjugate gradient method
• Nonmonotone backtracking inexact quasi-Newton algorithms for solving smooth nonlinear equations
• Nonmonotone adaptive trust-region method for unconstrained optimization problems
• A nonmonotone adaptive trust region method and its convergence
• An adaptive trust region method and its convergence
• A New Matrix-Free Algorithm for the Large-Scale Trust-Region Subproblem
• A New Modified Cholesky Factorization
• Computing a Trust Region Step
• The Conjugate Gradient Method and Trust Regions in Large Scale Optimization
• A Family of Trust-Region-Based Algorithms for Unconstrained Minimization with Strong Global Convergence Properties
• A Trust Region Algorithm for Equality Constrained Minimization: Convergence Properties and Implementation
• The “global” convergence of Broyden-like methods with suitable line search
• A Trust Region Algorithm for Nonlinearly Constrained Optimization
• Computing Optimal Locally Constrained Steps
• A Globally and Superlinearly Convergent Gauss--Newton-Based BFGS Method for Symmetric Nonlinear Equations
• A Practical Algorithm for General Large Scale Nonlinear Optimization Problems
• A Characterization of Superlinear Convergence and Its Application to Quasi-Newton Methods
• Benchmarking optimization software with performance profiles.

This page was built for publication: BFGS trust-region method for symmetric nonlinear equations