On the use of function-values in unconstrained optimisation
type: Item
instance of: scholarly article
title: On the use of function-values in unconstrained optimisation
zbMATH Open document ID: 0686.65031
DOI: 10.1016/0377-0427(89)90331-2
author: R.-A. Ghandhari
author: J. A. Ford
published in: Journal of Computational and Applied Mathematics
publication date: 1989-01-01T00:00:00Z
review text: By the use of a nonlinear model for the gradient of the objective function along a chosen direction it is shown how information in the form of function values may be utilised in optimization methods. The presented algorithmic outline provides a framework into which most ``quasi-Newton'' methods (for example, the DFP method, the BFGS method and the Hoshino method) may be fitted. The numerical experiments indicate that such an approach may lead to improvements in the performance of the BFGS algorithm, at the cost of the solution of a simple nonlinear equation in one variable at each iteration.
Mathematics Subject Classification ID: 65K05
Mathematics Subject Classification ID: 90C30
zbMATH DE Number: 4124906
zbMATH Keywords: unconstrained optimization
zbMATH Keywords: function values
zbMATH Keywords: quasi-Newton methods
zbMATH Keywords: DFP method
zbMATH Keywords: BFGS method
zbMATH Keywords: Hoshino method
zbMATH Keywords: numerical experiments
reviewed by: Nada Djuranović-Miličić
describes a project that uses: minpack
MaRDI profile type: Publication
full work available at URL: 0377-0427(89)90331-2
OpenAlex ID: W2071623988
cites work: Minimization Algorithms Making Use of Non-quadratic Properties of the Objective Function
cites work: A Note on Minimization Algorithms which make Use of Non-quardratic Properties of the Objective Function
cites work: A Comparison of Several Current Optimization Methods, and the use of Transformations in Constrained Problems
cites work: The Convergence of a Class of Double-rank Minimization Algorithms
cites work: Variable Metric Method for Minimization
cites work: Q3702408
cites work: A new approach to variable metric algorithms
cites work: Q4840579
cites work: A Rapidly Convergent Descent Method for Minimization
cites work: Q3818806
cites work: On the construction of minimization methods of quasi-Newton type
cites work: A Family of Variable-Metric Methods Derived by Variational Means
cites work: Q3135405
cites work: A Formulation of Variable Metric Methods
cites work: Modified Damped Least Squares: An Algorithm for Non-linear Estimation
cites work: Testing Unconstrained Optimization Software
cites work: Conditioning of Quasi-Newton Methods for Function Minimization
description: scientific article; zbMATH DE number 4124906