Numerical experiments on the conjugate gradient method with and without line search

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International Institute of Academic Research and Development


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.


Publication outlet: International Journal of Applied Science and Mathematical Theory 2(1), 1- 18


Conjugate gradient method,, Unconstrained optimization, Step-size without line search


Ajimoti and Bamigbola (2016)