Pattern search method: deterministic iterative zero order algorithm

It finds the relative minimum of a two variables function with the Pattern search method.

It's a deterministic iterative zero order algorithm that can be used to solve unconstrained optimization problem. It finds the relative minimum of a two variables function with a deterministic iterative zero order algorithm.

% Pattern search method
% It finds the relative minimum of a two variables function with the Pattern search method.
% The inputs are:
% - f: matlab inline function of the function that you want minimize;
% - p0: initial point for the search algorithm
% - step_size: initial step used for the exploration phase
% - tolerance: it defines a stopping criterion on the minimum size of exploration phase's step_size
% - N_it: it defines a stopping criterion on the max iterations number
% The outpus are:
% - iter: the number of iterations done
% - min: the function's value in the relative minimum finded.
% - p_min: it's a vector for the minimum point of the objective function

%%%% IMPORTANT: %%%%
for a correct work, the function 'pattern_search' must be preceded by a contour plot of the objective function to minimize.