An improved Wei-Yao-Liu nonlinear conjugate gradient method for optimization computation (Q1039699)

The author considers the unconstrained minimization problem consisting in a minimizing continuously differentiable function \(f\) defined on \(\mathbb{R}^n\). Conjugate gradient methods knows from the literature are compared and two slight modifications of \textit{Z. Wei}, \textit{S. Yao} and \textit{L. Liu}'s nonlinear conjugate method [Appl. Math. Comput. 183, No.~2, 1341--1350 (2006; Zbl 1116.65073)] are proposed. The modified methods posses better convergence properties and converge globally if the strong Wolfe line search with a restriction on one of its parameters is used. The second of the two methods is proved to be globally convergent even if the standard Wolfe line search is used. Numerical results reported in the concluding part of the paper show that the methods are efficient for problems from the CUTE library [see \textit{I. Bongartz}, \textit{A. R. Conn}, \textit{N. Gould} and \textit{Ph. L. Toint}, CUTE: constrained and unconstrained testing environments, ACM Trans. Math. Softw 21, No. 1, 123--160 (1995; Zbl 0886.65058)]. The efficiency of the proposed methods is compared with the efficiency of some other conjugate gradient methods.