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Two efficient nonlinear conjugate gradient methods. (Chinese. English summary) Zbl 1299.65120

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.

MSC:

65K05 Numerical mathematical programming methods
90C90 Applications of mathematical programming
90C52 Methods of reduced gradient type
90C30 Nonlinear programming

Software:

CUTEr
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