A Dai-Liao conjugate gradient method via modified secant equation for system of nonlinear equations. (English) Zbl 1445.90108
Summary: In this paper, we propose a Dai-Liao (DL) conjugate gradient method for solving a large-scale system of nonlinear equations. The method incorporates an extended secant equation developed from modified secant equations proposed by J. Z. Zhang et al. [J. Optim. Theory Appl. 102, No. 1, 147–167 (1999; Zbl 0991.90135)] and Z. Wei et al. [Appl. Math. Comput. 175, No. 2, 1156–1188 (2006; Zbl 1100.65054)] in the DL approach. It is shown that the proposed scheme satisfies the sufficient descent condition. The global convergence of the method is established under mild conditions, and computational experiments on some benchmark test problems show that the method is efficient and robust.
MSC:
| 90C30 | Nonlinear programming |
| 65K05 | Numerical mathematical programming methods |
| 90C53 | Methods of quasi-Newton type |
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