Nelder–Mead method
A derivative-free method that moves a triangle (or higher-dimensional simplex) of trial points toward a minimum by comparing function values alone.
The Nelder-Mead method maintains n+1 points (a simplex) in \mathbb R^n — a triangle for n=2 — and, each iteration, replaces the worst point by comparing its reflection through the centroid of the other points against the simplex's own function values, choosing to reflect, expand further, contract back, or (rarely) shrink the whole simplex toward its best vertex. No gradient or Hessian is ever computed; every decision uses only ordinary comparisons of f at the simplex's own vertices.
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