A comparison between line searches and trust regions for nonliner optimization

Line searches and trust regions are two techniques to globalize nonlinear optimization algorithms. The paper claims that the trust-region technique has built-in an appropriate regularization of ill-conditioned second-order approximation. The question asked and then answered in this short paper supports this claim. The paper forces the trust-region technique to act like a line search and it accomplishes this by always choosing the step along the quasi-Newton direction. The paper obtains global convergence to a stationary point as long as the condition number of the second-order approximation is uniformly bounded, a condition that is required in line searches but not in trust regions.