# Nonlinear Simplex Method

Nonlinear simplex method is an algorithm that may be appropriate when the gradient of $$f$$ is hard to calculate or when the function value contains noise. For an $$n$$-dimensional problem, the nonlinear simplex method maintains a simplex of $$n+1$$ points (a triangle in two dimensions or a pyramid in three dimensions). The simplex moves, expands, contracts, and distorts its shape as it attempts to find a minimizer. This method is slow and can be applied only to problems in which $$n$$ is small. It is, however, popular, since it requires the user to supply only function values, not derivatives.