Numerical experiments on the conjugate gradient method with and without line search
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Date
2016
Journal Title
Journal ISSN
Volume Title
Publisher
International Institute of Academic Research and Development
Abstract
The conjugate gradient method CGM is an effective iterative method which is widely
used for solving large-scale unconstrained optimization problems due to its low memory requirement. The efficiency of the CGM depends majorly on the step-size. Line search technique has been used in various literatures to obtain the step-size. A very recent development is to obtain the step-size with a unified formula which is refereed to as step-size without line search. Hence, in this work, we present numerical experiments for well-known CGMs such as Fletcher-Reeves, Bamigbola-Ali-Nwaeze, Polak-Ribiere, Dai-Yuan, Liu-Storey, Hesten-Stiefel, Conjugate-Descent, Hager-Zhang and Gradient Search Conjugacy methods. Numerical results obtained are graphically illustrated using performance profiling software to compare numerical efficiency of
five inexact line searches namely Armijo, Goldstein, Weak, Strong and Approximate Wolfe and two formulae for estimating the step-size without line search which are Wu formula and Ajimoti-Bamigbola formula.
Description
Publication outlet: International Journal of Applied Science and Mathematical Theory 2(1), 1- 18
Keywords
Conjugate gradient method,, Unconstrained optimization, Step-size without line search
Citation
Ajimoti and Bamigbola (2016)