A Sufficient Descent Property to Improving a ThreeTerm Conjugate Gradient Algorithm

Authors

  • Ghada M. al-Naemi
  • Firas Mahmood Saeed

DOI:

https://doi.org/10.29020/nybg.ejpam.v15i3.4437

Keywords:

TTCGM, nonlinear unconstrained optimization, SWPL search, SDP.

Abstract

The nonlinear conjugate gradient (NLCGM) methods have received attention because due to their simplicity, low memory requirements, and global convergent property, which allows them to be used directly to solve large-scale nonlinear unconstrained optimization problems. We suggested a modification to the β KMAR k formula, applied with three-term conjugate gradient method that is both simple and effective, denoted by (TTKMAR), which has a sufficient descent property (SDP) and ensures global convergence (GCP) when we use any line search. The numerical efficiency of TTKMAR was assessed using a variety of standard test functions. TTCGM has been demonstrated to be more numerically efficient than two-term CG methods. This paper also quantifies the difference between TTCGM and two-term methods of performance. As a result, we compare our new modification to an efficient two-term and TTCGM in the numerical results. Finally, we conclude that our proposed modification.

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How to Cite

al-Naemi, . G. M. ., & Saeed, F. M. . (2022). A Sufficient Descent Property to Improving a ThreeTerm Conjugate Gradient Algorithm. European Journal of Pure and Applied Mathematics, 15(3), 1254–1264. https://doi.org/10.29020/nybg.ejpam.v15i3.4437