Dogleg paths and trust region methods with back tracking technique for unconstrained optimization

In this paper, we improve approximate trust region methods via a class of dogleg paths for unconstrained optimization. The dogleg paths include both definite and indefinite ones. A hybrid strategy using both trust region and line search techniques is adopted which switches to back tracking steps when a trial step produced by the trust region subproblem is unacceptable. We show that the algorithm preserves the strong convergence properties of trust region methods. Numerical results are presented and discussed.