Some three-term conjugate gradient methods with the inexact line search condition

The three-term conjugate gradient methods solving large-scale optimization problems are favored by many researchers because of their nice descent and convergent properties. In this paper, we extend some new conjugate gradient methods, and construct some three-term conjugate gradient methods. An remarkable property of the proposed methods is that the search direction always satisfies the sufficient descent condition without any line search. Under the standard Wolfe line search, the global convergence properties of the proposed methods are proved merely by assuming that the objective function is Lipschitz continuous. Preliminary numerical results and comparisons show that the proposed methods are efficient and promising.