Different Types of Three-Term CG-Methods with Sufficient Descent and Conjugacy Conditions

Volume 16 , Issue 2 , April 2014 , Pages 27-45

Authors

¹ College of Telafer Basic Education, Mathematics, Mosul University

² College of Computer Sciences and Mathematics, Mathematics, Mosul University

It is very important to generate a descent search direction independent of line searches in

showing the global convergence of conjugate gradient methods. Recently, Zhang et al. proposed

a three-term of PR method (TTPR) and HS method (TTHS), both of which can produce

sufficient descent condition. In this paper, we treat two subjects: we first consider new unified

formula of three-term CG algorithm, second we suggested new scaled three-term algorithm

based on Birgin-Martínez algorithm and which satisfied both the descent and conjugacy

conditions are proposed. This algorithms are modification of the Hestenes-Stiefel and Birgin-

Martínez algorithms, also the algorithms could be considered as a modification of the

memoryless BFGS quasi-Newton method. Our algorithms can proved the global convergence

property and more efficiently than HS and BM algorithms in numerical results.

Statistics