In this paper, a new combined extended Conjugate-Gradient (CG) and Variable-Metric (VM) methods is proposed for solving unconstrained large-scale numerical optimization problems. The basic idea is to choose a combination of the current gradient and some pervious search directions as a new search direction updated by Al-Bayati's SCVM-method to fit a new step-size parameter using Armijo Inexact Line Searches (ILS). This method is based on the ILS and its numerical properties are discussed using different non-linear test functions with various dimensions. The global convergence property of the new algorithm is investigated under few weak conditions. Numerical experiments show that the new algorithm seems to converge faster and is superior to some other similar methods in many situations.
Al-Bayati, Abbas Y. and Latif, Ivan S.
A New CG-Algorithm with Self-Scaling VM-Update for Unconstraint Optimization,
Applications and Applied Mathematics: An International Journal (AAM), Vol. 7,
1, Article 16.
Available at: https://digitalcommons.pvamu.edu/aam/vol7/iss1/16