Is normalization of input variables necessary for problem using second order algorithms?

Question

I have a question about normalizing input variables in optimization. While it's widely acknowledged that normalization is crucial for first-order optimization algorithms like gradient descent, I'm uncertain about its necessity for second-order algorithms such as L-BFGS-B or Newton's method, as well as Conjugate Gradient (CG), which has the ability to search fully in one direction. Could someone provide insights into whether variable normalization is essential when using these second-order optimization techniques? I appreciate any clarification on this matter. Thank you.