feat: use hessian in optimization

[john-halloran]

A hessian was the one feature I had left out of the original port because I was having issues with it, but as I go on I've realized that it's not optional. Without it, there is too much instability to write reliable tests. Those are ongoing, by the way, but I wanted to open this PR in the meantime.

[sbillinge]

its very hard for me to review this as I am really hazy about what is going on. I am happy to trust you on this. Just let me know if you want it merged.

[john-halloran]

To be honest, I am hazy on the mathematical details as well. I did some pretty thorough checks, printing out matrices at each step of the process to make sure that they match the MATLAB, but I feel a little out of my depth, especially when it comes to resolving some of the remaining discrepancies that I've noticed. Do you know anyone who could be reached out to so we can give the code a second look?

[sbillinge]

I think if you are able to print out matrices and check htey are the same as the matlab code, it is already rather careful. We could, if we want, capture these as tests. Place the matlab matrix as expected and the matrix produced by your function as actual. That means that this hard work survives into the future and keeps working for us.

At the end we can ask Ran to look it over, but he is not a Python person so he won't give programming insights, but he will have some idea if it is working ok on a larger scale.

[john-halloran]

Closing for now because this is not the right branch.