Nelder-Mead Method Algorithm

The Nelder-Mead method searches for a local minimum of a function of several variables without using any derivative information, by maintaining a simplex, a shape with one more vertex than the number of dimensions, and repeatedly replacing its worst vertex through operations called reflection, expansion, contraction and shrinkage that move the simplex downhill across the function's surface toward a minimum. John Nelder and Roger Mead published the method in 1965. It remains widely used as a simple, derivative-free optimization technique, though it offers no guarantee of convergence to a true minimum on all functions and can stall on some problem shapes.