Convergence properties of the Fletcher-Reeves method

Published on Apr 1, 1996in Ima Journal of Numerical Analysis2.601
· DOI :10.1093/IMANUM/16.2.155
Yu-Hong Dai37
Estimated H-index: 37
 , Ya-xiang Yuan35
Estimated H-index: 35
Sources
Abstract
This paper investigates the global convergence properties of the Fletcher-Reeves (FR) method for unconstrained optimization. In a simple way, we prove that a kind of inexact line search condition can ensure the convergence of the FR method. Several examples are constructed to show that, if the search conditions are relaxed, the FR method may produce an ascent search direction, which implies that our result cannot be improved.
đź“– Papers frequently viewed together
19641.49The Computer Journal
2 Authors (Roger Fletcher, C. M. Reeves)
1969Ussr Computational Mathematics and Mathematical Physics
1 Author (Boris T. Polyak)
19852.60Ima Journal of Numerical Analysis
1 Author (M. Al-Baali)
References0
Newest
Cited By90
Newest
Multivariate binary data are increasingly frequent in practice. Although some adaptations of principal component analysis are used to reduce dimensionality for this kind of data, none of them provide a simultaneous representation of rows and columns (biplot). Recently, a technique named logistic biplot (LB) has been developed to represent the rows and columns of a binary data matrix simultaneously, even though the algorithm used to fit the parameters is too computationally demanding to be useful...
Source
Source
Nov 6, 2020·arXiv: Optics
#1Özüm Emre Aşırım (METU: Middle East Technical University)H-Index: 4
#2Alim YolalmazH-Index: 3
Optical amplification of the input wave by mixing the pump wave within a nonlinear interaction medium offers high gain for a variety of applications. In real life studies, the interaction mediums which allow the optical amplification of the input wave have many resonance frequencies. However, the computational expense for tuning the pump frequency to yield the optical amplification of the input wave increases with the number of resonance frequencies within the interaction mediums. Here, we prese...
Sep 1, 2020·Iranian Journal of Science and Technology-Transactions of Mechanical Engineering1.60
#1Vahid Shokouhifard (Persian Gulf University)H-Index: 1
#2Saeedreza Mohebpour (RyeU: Ryerson University)
Last. Mohammadreza Golbaharhaghighi (Persian Gulf University)
view all 4 authors...
In this paper, the use of the inverse solution method for estimating the mass of moving load on an inclined functionally graded material (FGM) Timoshenko beam is discussed based on the measured displacements. Fletcher–Reeves (FR) method is used to solve the inverse problem. Also, in the process of solving the inverse problem and in order to solve the direct problem, Newmark method is applied for discretization of the time domain and finite element method (FEM) is used for discretization of the s...
Source
#1Ibrahim Mohammed Sulaiman (UniSZA: Universiti Sultan Zainal Abidin)H-Index: 6
#2Mustafa Mamat (UniSZA: Universiti Sultan Zainal Abidin)H-Index: 16
Last. Maulana MalikH-Index: 4
view all 6 authors...
Source
#2Lin Cao (Qilu University of Technology)H-Index: 1
Source
#1Hadi NosratipourH-Index: 3
#2Keyvan AminiH-Index: 12
Apr 1, 2019·Applied Mathematical Modelling5.13
#1K. Cao (University of Leeds)H-Index: 1
#2Daniel Lesnic (University of Leeds)H-Index: 39
Abstract Inverse coefficient identification formulations give rise to some of the most important mathematical problems because they tell us how to determine the unknown physical properties of a given medium under inspection from appropriate extra measurements. Such an example occurs in bioheat transfer where the knowledge of the blood perfusion is of critical importance for calculating the temperature of the blood flowing through the tissue. Furthermore, in many related applications the initial ...
Source
In this paper, we present a new hybrid conjugate gradient algorithm for unconstrained optimization. This method is a convex combination of Liu-Storey conjugate gradient method and Fletcher-Reeves conjugate gradient method. We also prove that the search direction of any hybrid conjugate gradient method, which is a convex combination of two conjugate gradient methods, satisfies the famous D-L conjugacy condition and in the same time accords with the Newton direction with the suitable condition. Fu...
Source
Jul 1, 2018·Numerical Algorithms3.04
#1Wenling Zhao (SDUT: Shandong University of Technology)
#2Changyu Wang (Qufu Normal University)
Last. Yajing Gu (SDUT: Shandong University of Technology)
view all 3 authors...
In this paper, the authors present an s-dependent conjugate gradient method for unconstrained optimization problem and make two different kinds of estimations of upper bounds of β k with respect to \(\beta_{k}^{\mathrm{FR}}\) which are called dependent ratio. The global convergence of s-dependent GFR conjugate gradient method using several step-size rules is obtained.
Source
123456789
This website uses cookies.
We use cookies to improve your online experience. By continuing to use our website we assume you agree to the placement of these cookies.
To learn more, you can find in our Privacy Policy.