A Limited BFGS Trust-region Method with a New Nonmonotone Technique for Nonlinear Equations

Meihong Zhou, Qinghua Zhou*

College of Mathematics and Information Science, Hebei University, Baoding, 071002, China

Abstract: In this paper, we incorporate a nonmonotone technique with the new proposed adaptive trust region radius for solving the nonlinear equations. To decrease the computational complexity, a limited memory BFGS ｕｐｄａｔｅ is used to generate an approximated matrix rather than a normal Jacobian matrix ｏｒ quasi- Newton matrix. Moreover, a line search technique is used to avoid repeatedly computing the trust region algorithm. Theoretical analysis indicates that the new method preserves the global convergence under mild conditions.

Keywords: Nonlinear equations; Trust region method; Nonmonotone strategy; Limited memory BFGS method; Global convergence