title: A Limited-Memory BFGS Algorithm Based on a Trust-Region Quadratic Model for Large-Scale Nonlinear Equations.
abstract: In this paper, a trust-region algorithm is proposed for large-scale nonlinear equations, where the limited-memory BFGS (L-M-BFGS) update matrix is used in the trust-region subproblem to improve the effectiveness of the algorithm for large-scale problems. The global convergence of the presented method is established under suitable conditions. The numerical results of the test problems show that the method is competitive with the norm method.
authors.affiliation: Department of Mathematics, Baise University, Baise, Guangxi, P. R. China.
authors.forename: Yong
authors.initials: Y
authors.lastname: Li
authors.affiliation: College of Mathematics and Information Science, Guangxi University, Nanning, Guangxi, P.R.China.
authors.forename: Gonglin
authors.initials: G
authors.lastname: Yuan
authors.affiliation: College of Mathematics and Information Science, Guangxi University, Nanning, Guangxi, P.R.China.
authors.forename: Zengxin
authors.initials: Z
authors.lastname: Wei
mesh_terms: D000465:Algorithms; D008962:Models, Theoretical; D017711:Nonlinear Dynamics