Liu, Jinkui Two efficient nonlinear conjugate gradient methods. (Chinese. English summary) Zbl 1299.65120 Math. Numer. Sin. 35, No. 3, 286-296 (2013). Summary: By the structure of the conjugate gradient descent (CG-DESCENT) method by W. W. Hager et al.’s [SIAM J. Optim. 16, No. 1, 170–192 (2005; Zbl 1093.90085)] and M. J. D. Powell’s suggestion [SIAM Rev. 28, 487–500 (1986; Zbl 0624.90091)], two efficient nonlinear conjugate gradient methods are given. The given methods can be guaranteed the sufficient descent property without any line search, and be proved the global convergence property for the general functions under the standard Wolfe line search. In particular, by the famous evaluation method of E. D. Dolan and J. J. MorĂ© [Math. Program. 91, No. 2 (A), 201–213 (2002; Zbl 1049.90004)], the numerical results also show that the proposed methods are more efficient by comparing with the famous CG-DESCENT method using a classical set of problems from CUTEr library. Cited in 1 ReviewCited in 3 Documents MSC: 65K05 Numerical mathematical programming methods 90C90 Applications of mathematical programming 90C52 Methods of reduced gradient type 90C30 Nonlinear programming Keywords:nonlinear conjugate gradient method: standard Wolfe line search; sufficient descent property; global convergence; conjugate gradient descent method; numerical results Citations:Zbl 1093.90085; Zbl 0624.90091; Zbl 1049.90004 Software:CUTEr PDFBibTeX XMLCite \textit{J. Liu}, Math. Numer. Sin. 35, No. 3, 286--296 (2013; Zbl 1299.65120)