Here are the links from today's meeting:

Lucy Martin et al.'s IBEX paper
https://arxiv.org/abs/1812.03761
https://iopscience.iop.org/article/10.1088/1367-2630/ab0e28

Levenberg-Marquardt algorithm for multi-parameter optimisation (called least squares fit here).  I've used it successfully with 120 parameters to make a beam focus corrected to multiple orders.
https://en.wikipedia.org/wiki/Levenberg%E2%80%93Marquardt_algorithm

     -Stephen