On Jorge Nocedal's , Page 501, "This property alone is enough to make many unconstrained minimization algorithms such as quasi-Newton and conjugate gradient perform poorly. Newton’s method, on the other hand, is not sensitive to ill conditioning of the Hessian". Can any one give a more detailed analysis?
"An ill conditioned hessian means that the gradient is changing direction rapidly; this causes a problem because our method is only looking at the gradient at one point. Newton's method is solving this problem because it looks at the hessian and is taking the rate of change of the gradient into account."