A New Type Of Trust Region Method

In this paper, we propose two improved trust region methods for solving unconstrainedoptimization problems. Different with traditional trust region methods, both the improvedtrust region algorithms do not resolve the subproblem within the trust region centered at thecurrent iteration point, but within an improved one centered at some point located in thedirection of the negative gradient. We prove the global convergence properties of the newimproved trust region algorithm and give the computational results which demonstrate theeffectiveness of our algorithm.