I am trying to solve a system of $9$ polynomial equations in $9$ unknowns over the non-negative reals.


Since the equations are quite large and I would like to use VBA, I prefer an algorithm that avoids partial derivatives. Hence, I tried to use the [Nelder-Mead](https://en.wikipedia.org/wiki/Nelder%E2%80%93Mead_method) (downhill simplex) algorithm. Unfortunately, it doesn't converge. Before investigating my code, I would like to know if [Nelder-Mead](https://en.wikipedia.org/wiki/Nelder%E2%80%93Mead_method) is even suitable for my task. If not, could you recommend a better algorithm?


P. S. I already solved the problem using Mathematica, so it is solvable but I would like to implement it in MS Excel.



Using Nelder-Mead to solve system of polynomial equations
Minimum-finding routines (which is what Nelder-Mead/downhill-simplex is) are generally poorly suited to finding zeros of equation systems — if you add the squares of all equations, you get many spurious local minima in addition to the global minimum corresponding to the zero (assuming your equations have a unique zero).


If you can't afford to evaluate the Jacobian, your best hope would appear to be [Broyden's method](https://en.wikipedia.org/wiki/Broyden%27s_method).


