A New Modified Three-Term Conjugate Gradient Method with Sufficient Descent Property and Its Global Convergence

• Main Authors: Bakhtawar Baluch, Zabidin Salleh, Ahmad Alhawarat, U. A. M. Roslan
• Format: Article
• Language: English
• Published: Hindawi Limited 2017-01-01
• Series: Journal of Mathematics
• Online Access: http://dx.doi.org/10.1155/2017/2715854

A new modified three-term conjugate gradient (CG) method is shown for solving the large scale optimization problems. The idea relates to the famous Polak-Ribière-Polyak (PRP) formula. As the numerator of PRP plays a vital role in numerical result and not having the jamming issue, PRP method is not globally convergent. So, for the new three-term CG method, the idea is to use the PRP numerator and combine it with any good CG formula’s denominator that performs well. The new modification of three-term CG method possesses the sufficient descent condition independent of any line search. The novelty is that by using the Wolfe Powell line search the new modification possesses global convergence properties with convex and nonconvex functions. Numerical computation with the Wolfe Powell line search by using the standard test function of optimization shows the efficiency and robustness of the new modification.