Abstract: In this paper,a new trust region algorithrn for unconstrained LC'optimization problems is given.Compare with those existing trust region methods,this algorithm has a different feature:it ob- tains a stepsize at each iteration not by soloving a quadratic subproblem with a trust region bound,but by solving a system of linear equations.Thus it reduces computational complexity and improves compu-  tation efficlency.It is proven that this algorithm is globally convergent and locally superlinear under some conditions.

Key words: LC'optimization;ODE , methods;trust , region ,  algorithm;superlinear ,  convergence