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minimization of a function by random iterative search

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Optimization method: Locates a minimum of a target function. Converges to global optimum.

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function vopt = min_by_random_search( fnc, region )
Minimization of a function by iterative random search.
Written by Dr. Yoash Levron, February 2013.

This function implements a minimization algorithm, based on iterative random search. At each iteration, the function randomize vectors in the search region, and finds the one that minimizes the target function. Then, a smaller search
region is defined around this minimizer. The process repeats itself, shrinking the search region until convergence.

This algorithm converges slower than gradient based algorithm, but it has several advantages:
a) It does not require a specific derivative.
b) It converges to a global optimum, even if the function holds many local ones.

The algorithm works well with functions of relatively low dimension: up to about 10-20 variables. If the dimension is too high, the function may fail to locate a global minimum.
A useful test is to run the function a few times, checking that it locates the same optimum.

inputs:
fnc - A handle to the target function to be minimized.
region - 2*N matix specifying the region of search. It specifies a range for each of the function variables.
region(1,n) - is the low bound for variable n
region(2,n) - is the high bound for variable n

outputs:
vopt - (N*1), the minimizing vector.

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