A Relationship between the BFGS and Conjugate Gradient Algorithms and Its Implications for New Algorithms

DOI10.1137/0716059zbMath0424.65030OpenAlexW2059808679MaRDI QIDQ3859201

Larry Nazareth

Publication date: 1979

Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/0716059

zbMATH Keywords

algorithmsvariable metric algorithmsBroyden-Fletcher-Goldfarb-Shanno algorithmconjugate gradient algorithmsminimum of an unconstrained function

Mathematics Subject Classification ID

Numerical mathematical programming methods (65K05) Nonlinear programming (90C30) Quadratic programming (90C20)

Related Items (21)

A novel class of approximate inverse preconditioners for large positive definite linear systems in optimization ⋮ A compact limited memory method for large scale unconstrained optimization ⋮ On accelerating Newton's method based on a conic model ⋮ Two modified scaled nonlinear conjugate gradient methods ⋮ Regularization of limited memory quasi-Newton methods for large-scale nonconvex minimization ⋮ Preconditioned nonlinear conjugate gradient methods based on a modified secant equation ⋮ Conjugate direction methods and polarity for quadratic hypersurfaces ⋮ Some numerical experiments with variable-storage quasi-Newton algorithms ⋮ On the limited memory BFGS method for large scale optimization ⋮ Conjugate gradient methods using quasi-Newton updates with inexact line searches ⋮ Unnamed Item ⋮ Some remarks on conjugate gradient methods without line search ⋮ On exact linesearch quasi-Newton methods for minimizing a quadratic function ⋮ Novel preconditioners based on quasi-Newton updates for nonlinear conjugate gradient methods ⋮ Oblique projections, Broyden restricted class and limited-memory quasi-Newton methods ⋮ Near real-time atmospheric contamination source identification by an optimization-based inverse method ⋮ A variation of Broyden class methods using Householder adaptive transforms ⋮ QN-like variable storage conjugate gradients ⋮ On the connection between the conjugate gradient method and quasi-Newton methods on quadratic problems ⋮ Conjugate direction methods with variable storage ⋮ On diagonally-preconditioning the 2-step BFGS method with accumulated steps for linearly constrained nonlinear programming

This page was built for publication: A Relationship between the BFGS and Conjugate Gradient Algorithms and Its Implications for New Algorithms