NLLS stands for nonlinear least-squares and SQP is sequential quadratic programming. So essentially this is an optimization problem, and everyone knows that NAG Library's chapter e04 is the best place to look for optimization solvers. The appropriate NAG routine in our C Library is nag_opt_nlin_lsq (e04unc).
A few weeks ago one of our users contacted NAG and asked for an example program of using e04unc in Excel. NAG and Excel page has quite a few examples and guidelines about using NAG Library in Excel, but we didn't have this particular one.
I wrote this example and now it is available for download on the Excel page. I encourage readers of this blog to download it and play with it on your own. It wasn't difficult to create it, but there was one issue that caused me a nasty headache. Some routines that have callback functions (just as e04unc does) where a vector or matrix is passed to/from a subroutine require usage of Windows API subroutine RtlMoveMemory.