A Limited-Memory BFGS Algorithm Based on a Trust-Region Quadratic Model for Large-Scale Nonlinear Equations A Limited-Memory BFGS Algorithm Based on a Trust-Region Model

Abstract

Title: A Limited-Memory BFGS Algorithm Based on a Trust-Region Quadratic Model for Large-Scale Nonlinear Equations A Limited-Memory BFGS Algorithm Based on a Trust-Region Model Authors: ['Yong Li' 'Gonglin Yuan' 'Zengxin Wei' 'Zi-Ke Zhang'] 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.