I'd like to use Monte Carlo (if it's useful to know, the
Numpy Monte Carlo tools) to solve (arbitrary) nonlinear systems of equations where a solution might otherwise be given by optimization techniques such as least-squares minimization, etc.
I know it to be possible, however I've never used Monte Carlo in this way, nor have I used the
Numpy Monte Carlo tools. How might Monte Carlo be applied to such a task and, more importantly, why does it work, intuitively?
Unfortunately, I cannot find much out there on this topic, and what I have found lacks detail and is somewhat 'hand-wavy'. I'd like to understand it on a deeper level than "it just works".