# why Newton's method is not sensitive to ill-conditioned Hessian?

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?

• Hi: Newton's method doesn't use any information regarding the second derivative so that's why it's insensitive to it. It's a method that only relies on the first derivative. This is not the case for quasi-Newton and conjugate gradient methods. Jan 8 '19 at 6:23
• @mlofton: ?????????????????????? Jan 8 '19 at 9:26
• @kjeitil b halvorsen: I thought what I said was the case. if not, I'll delete comment. Jan 9 '19 at 15:37
• @mlofton Newton's method is a second order optimization method, which means it does in fact use the second derivative and as such computes (and inverts) the hessian directly. Newton-CG on the other hand solves a system of equations to 'invert' the hessian. All second order methods use the Hessian or at least some approximation. Jun 28 at 15:59
• oops: my mistake. I thought it just used the first derivative. thanks for heads up. should I delete my totally wrong comment-statement. Jun 28 at 18:11