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. (c) 2005 Elsevier Inc. All rights reserved.