Non-linear non-constrained minimization of a function

defined on an n-dimensional Euclidean space, using the Nelder-Mead method, also known as downhill simplex method. The basic idea about the method can be obtained from Nelder-Mead method.

It should be noted, that this method, although deterministic, is rather a heuristic and therefore may converge to a local minima, not necessary a global one. It is iterative optimization technique, which at each step uses an information about the values of a function evaluated only at n+1 points, arranged as a simplex in n-dimensional space (hence the second name of the method). At each step new point is chosen to evaluate function at, obtained value is compared with previous ones and based on this information simplex changes it's shape, slowly moving to the local minimum. Thus this method is using only function values to make decision, on contrary to, say, Nonlinear Conjugate Gradient method (which is also implemented in OpenCV).

Algorithm stops when the number of function evaluations done exceeds Termcrit.maxCount, when the function values at the vertices of simplex are within Termcrit.epsilon range or simplex becomes so small that it can enclosed in a box with Termcrit.epsilon sides, whatever comes first, for some defined by user positive integer Termcrit.maxCount and positive non-integer Termcrit.epsilon.

NOTE: term criteria should meet the following conditions:

• type == 'Count+EPS' && epsilon > 0 && maxCount > 0