Three-Term Conjugate Gradient (TTCG) methods

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. [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. [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. [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 .