It's mostly based on this:
Rosenbrock, H. H. (1960), "An automatic method for finding the
greatest or least value of a function", The Computer Journal 3:
175–184, DOI:10.1093/comjnl/3.3.175, ISSN 0010-4620, MR0136042
(Fifty-year old cutting-edge tech, eh?)
It's not pure, though. I found it beneficial to occasionally take a
few tentative Newton iterations based on numerical derivation. This
is useful because Newton iteration is very, very fast when
sufficiently close to the root.
So there. Nothing really fancy.
Note, that this is all in a plugin ("nlsolve") so if anyone feels like
writing another algorithm up for a solver, it's not that much work.
This one is ~800 lines.
Morten
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