I see several textbooks or blogs write that "trust region is dual method to line search", I can't agree with it. I think trust region is a superior method to line search because it's a quadratic approximation to the original function rather than a linear approximation, besides, it defines a region which parameters can't jump out of. Linear search actually has implicitly defined a region for step dt such that f(x+dt)>=0. If min{f(x)} < 0, we should define a trust region for linear search. Am I right or I have ignored something?
how to answer this question What is the main motivation behind Trust region methods? What could be a signal to enlarge the Trust region in the next step? What is the Cauchy point?
