"Combining trust region and line search techniques"
J. Nocedal, Y. Yuan.
Advances in Nonlinear Programming, ed. Y. Yuan, pp. 153-175 Kluwer (1998)
We propose an algorithm for nonlinear optimization that employs both trust region techniques and line searches. Unlike traditional trust region methods, our algorithm does not resolve the subproblem if the trial step results in an increase in the objective function, but instead performs a backtracking line search from the failed point. Backtracking can be done along a straight line or along a curved path. We show that the new algorithm preserves the strong convergence properties of trust region methods. Numerical results are also presented.