A Cauchy point direction trust region algorithm for nonlinear equations (Q2007093)

Summary: In this paper, a Cauchy point direction trust region algorithm is presented to solve nonlinear equations. The search direction is an optimal convex combination of the trust region direction and the Cauchy point direction with the sufficiently descent property and the automatic trust region property. The global convergence of the proposed algorithm is proven under some conditions. The preliminary numerical results demonstrate that the proposed algorithm is promising and has better convergence behaviors than the other two existing algorithms for solving large-scale nonlinear equations.