Different Types of Three-Term CG-Methods with Sufficient Descent and Conjugacy Conditions - Al-Bayati, Abbas Y.; Al-Khayat, Hawraz N. (Sulaimani Journal for Pure and Applied Sciences, 2014)
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.
Keywords: ThreeTerm Conjugate Gradient; Global Convergence; Unconstrained Optimization,Descent Direction; Conjugacy Condition; Memoryless BFGS