Nonmonotone spectral method for large-scale symmetric nonlinear equations

DOI10.1007/s11075-012-9572-zzbMath1259.65076OpenAlexW1977459204MaRDI QIDQ1938081

Wanyou Cheng, Zixin Chen

Publication date: 1 February 2013

Published in: Numerical Algorithms (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11075-012-9572-z

zbMATH Keywords

global convergencenumerical resultssteepest descentspectral methodnonmonotone line searchsymmetric nonlinear equations

Mathematics Subject Classification ID

Numerical computation of solutions to systems of equations (65H10)

Related Items

A new nonmonotone spectral residual method for nonsmooth nonlinear equations ⋮ An efficient modified residual-based algorithm for large scale symmetric nonlinear equations by approximating successive iterated gradients ⋮ Gradient-based method with active set strategy for $\ell _1$ optimization ⋮ Unnamed Item ⋮ A Riemannian nonmonotone spectral method for self-adjoint tangent vector field ⋮ Norm descent conjugate gradient methods for solving symmetric nonlinear equations ⋮ A derivative-free conjugate gradient method and its global convergence for solving symmetric nonlinear equations ⋮ A nonmonotone PRP conjugate gradient method for solving square and under-determined systems of equations ⋮ An approach based on dwindling filter method for positive definite generalized eigenvalue problem ⋮ Nomonotone spectral gradient method for sparse recovery

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• A PRP type method for systems of monotone equations
• Globally convergent inexact quasi-Newton methods for solving nonlinear systems
• Practical quasi-Newton methods for solving nonlinear systems
• Recent progress in the global convergence of quasi-Newton methods for nonlinear equations
• Spectral gradient projection method for solving nonlinear monotone equations
• A family of derivative-free conjugate gradient methods for large-scale nonlinear systems of equations
• A Globally Convergent Newton-GMRES Subspace Method for Systems of Nonlinear Equations
• A descent modified Polak–Ribière–Polyak conjugate gradient method and its global convergence
• A Family of Quasi-Newton Methods for Nonlinear Equations with Direct Secant Updates of Matrix Factorizations
• The “global” convergence of Broyden-like methods with suitable line search
• Two-Point Step Size Gradient Methods
• Global Convergence Properties of Conjugate Gradient Methods for Optimization
• Quasi-Newton Methods, Motivation and Theory
• Convergence Theory of Nonlinear Newton–Krylov Algorithms
• A nonmonotone hybrid method for nonlinear systems^∗
• A derivative-free line search and global convergence of Broyden-like method for nonlinear equations
• Nonmonotone Spectral Methods for Large-Scale Nonlinear Systems
• A Globally and Superlinearly Convergent Gauss--Newton-Based BFGS Method for Symmetric Nonlinear Equations
• A Nonmonotone Line Search Technique for Newton’s Method
• Descent Directions of Quasi-Newton Methods for Symmetric Nonlinear Equations
• A Class of Methods for Solving Nonlinear Simultaneous Equations
• A Two-Term PRP-Based Descent Method
• Spectral residual method without gradient information for solving large-scale nonlinear systems of equations
• The cyclic Barzilai-–Borwein method for unconstrained optimization
• The conjugate gradient method in extremal problems
• A modified BFGS method and its global convergence in nonconvex minimization
• Benchmarking optimization software with performance profiles.
• Adaptive two-point stepsize gradient algorithm