Difficulty in applying search optimization

Difficulty in applying search optimization

I have a 3D data vector and I need to do optimization such that I get the
minimum among all the data. Let the data be Z =
0.3 0.1 0.9
1.2 0.84 0.3
9.312 0.18 1.9
and so on. Z is generated by a function Z = f(a,b,c) ie by putting the
values of a,b,c into some equation. Then, for a particular set of (a,b,c)
Z is calculated. So, the way the algo works is that
Iteration 1 : I found out the L2 norm of Z and did random search. The
minima value along with the a,b,c which gave them are recorded.
At iteration 2: Another new set of a,b,c are used and Z is recalculated.
This continues till all a,b,c have been substituted in Z.
This process of random search takes a lot of computation time if the array
size is huge (5000 data points). Therefore, I wanted to apply Newton's
method On Z but I just cannot understand how to do it as there is no
functional form or equation representation. Can somebody please explain
with code how to apply optimization so that the search process is
optimized and a global single minima across all dimension is obtained.