Enhanced Dai-Liao conjugate gradient methods for systems of monotone nonlinear equations. (English) Zbl 1476.65109
Summary: In this paper, we propose two conjugate gradient methods for solving large-scale monotone nonlinear equations. The methods are developed by combining the hyperplane projection method by M. V. Solodov and B. F. Svaiter [Appl. Optim. 22, 355–369 (1999; Zbl 0928.65059)] and two modified search directions of the famous method of Y. H. Dai and L. Z. Liao [Appl. Math. Optim. 43, No. 1, 87–101 (2001; Zbl 0973.65050)]. It is shown that the proposed schemes satisfy the sufficient descent condition. The global convergence of the methods are established under mild conditions, and computational experiments on some benchmark test problems show that the methods are promising.
MSC:
| 65K05 | Numerical mathematical programming methods |
| 90C30 | Nonlinear programming |
| 90C53 | Methods of quasi-Newton type |
| 49M37 | Numerical methods based on nonlinear programming |
| 15A18 | Eigenvalues, singular values, and eigenvectors |
Keywords:
nonlinear equations; eigenvalue analysis; hyperplane projection; monotonicity property; global convergenceReferences:
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