Nonlinear Simplex Method

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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.