## Nelder-Mead Simplex Optimization

The Nelder-Mead-Algorithm (also known as the “Simplex Algorithm” or even
as the “Amoeba Algorithm”) is an algorithm for the minimization of
non-linear functions in several variables. In contrast to other non-linear
minimization methods, it does *not* require gradient information. This
makes it less efficient, but also less prone to divergence problems. In
contrast to other methods, it is *not* necessary for the minimum to be
bracketed by the initial guess: the algorithm performs a limited “global”
search. (It may still converge to a local, rather than the global extremum,
of course.) Finally, the algorithm is fairly simple to implement as a
stand-alone routine, which makes it a natural choice for multi-dimensional
minimization *if function evaluations are not prohibitively expensive*.