Conjugate gradient (CG)-type method for the solution of Newton's equation within optimization frameworks

DOI10.1080/10556780410001689234zbMath1141.90541OpenAlexW2161756383MaRDI QIDQ4657813

Giovanni Fasano

Publication date: 14 March 2005

Published in: Optimization Methods and Software (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/10556780410001689234

zbMATH Keywords

conjugate gradient methodKrylov subspace methodslarge-scale unconstrained optimizationNewton's equation

Mathematics Subject Classification ID

Numerical mathematical programming methods (65K05) Nonlinear programming (90C30) Methods of reduced gradient type (90C52)

Related Items (5)

Iterative grossone-based computation of negative curvature directions in large-scale optimization ⋮ Conjugate direction methods and polarity for quadratic hypersurfaces ⋮ A Class of Approximate Inverse Preconditioners Based on Krylov-Subspace Methods for Large-Scale Nonconvex Optimization ⋮ Polarity and conjugacy for quadratic hypersurfaces: a unified framework with recent advances ⋮ Planar methods and grossone for the conjugate gradient breakdown in nonlinear programming

Uses Software

• Bi-CG
• tn

Cites Work

• Unnamed Item
• A truncated Newton method with non-monotone line search for unconstrained optimization
• A composite step bi-conjugate gradient algorithm for nonsymmetric linear systems
• Iterative solution of linear systems in the 20th century
• A survey of truncated-Newton methods
• Truncated-Newton algorithms for large-scale unconstrained optimization
• Solution of Sparse Indefinite Systems of Linear Equations
• Curvilinear Stabilization Techniques for Truncated Newton Methods in Large Scale Unconstrained Optimization
• CUTE
• Exploiting negative curvature directions in linesearch methods for unconstrained optimization
• Solving the Trust-Region Subproblem using the Lanczos Method
• Iterative Solution Methods
• Hyperbolic Pairs in the Method of Conjugate Gradients
• Partial Pivoting Strategies for Symmetric Matrices
• Methods of conjugate gradients for solving linear systems

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