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

Authors

  • Abbas Y. Al-Bayati College of Telafer Basic Education, Mathematics, Mosul University, Kurdistan Region, Iraq. Author
  • Hawraz N. Al-Khayat College of Computer Sciences and Mathematics, Mathematics, Mosul University, Kurdistan Region, Iraq. Author

DOI:

https://doi.org/10.17656/jzs.10291

Keywords:

Three-Term Conjugate Gradient, Global Convergence, Unconstrained Optimization, Descent Direction, Conjugacy Condition, Memoryless BFGS

Abstract

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.

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Published

2014-04-24

How to Cite

Different Types of Three-Term CG-Methods with Sufficient Descent and Conjugacy Conditions. (2014). Journal of Zankoy Sulaimani - Part A, 16(2), 27-45. https://doi.org/10.17656/jzs.10291

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