Vicente, Luís N.2018-06-182018-06-181995-04Vicente, Luís N.. "What Happens When We Trust a Region That is a Line?." (1995) <a href="https://hdl.handle.net/1911/101855">https://hdl.handle.net/1911/101855</a>.https://hdl.handle.net/1911/101855Line searches and trust regions are two techniques to globalize nonlinear optimization algorithms. We claim that the trust-region technique has built-in an appropriate regularization of ill-conditioned second-order approximation. The question we ask and then answer in this short paper supports this claim. We force the trust-region technique to act like a line search and we accomplish this by always choosing the step along the quasi-Newton direction. We obtain global first-order convergence 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.8 ppengTechnical reportTR95-10