Three-Term Conjugate Gradient (TTCG) methods

Yıl 2019, Cilt: 2 Sayı: 1, 16 - 26, 02.08.2019

Zeyad M. Abdullah , Marwan S. Jameel

Öz

In this study, a comprehensive hybrid the formula was developed for some known algorithms of “Three-Term Conjugate
Gradient (TTCG) methods” for solving problems of unconstrained optimization by
combining the three most important vectors () in a new vector . In addition,
it is considered as a special case and as an alternative to the vector  in the general
versions of Yasushi, Yabe, and Ford. Global convergence, sufficient descend and
conjugacy were studied in the presence of strong Wolfe. The results proved the
efficiency of proposed algorithms than comparative algorithms using 35
nonlinear functions.

Anahtar Kelimeler

Unconstrained Optimization, Conjugate Gradient, Global convergence

Kaynakça

• [1] L. Zhang, W. Zhou and D.H. Li, "A descent modified Polak-Ribi`ere-Polyak conjugate gradient method and its global convergence ", IMA Journal of Numerical Analysis, 26 (2006),629–640.
• [2] L. Zhang, W. Zhou and D.H. Li, "Global convergence of a modified Fletcher-Reeves conjugate gradient method with Armijo-type line search", Numerische Mathematik, 104 (2006),561–572.
• [3] L. Zhang, W. Zhou and D.H. Li, Some descent three-term conjugate gradient methods and their global convergence, Optimization Methods and Software, 22 (2007), 697–711 .