Issues in applying simulated annealing

Issues in applying simulated annealing

Problem Statement : I have 2 vectors a,b each consisting of 50 random
values generated by say a= 0.25+0.001; b=0.35+0.001. These are substituted
into an equation say AR model z(t) = a*z(t-1) + b*z(t-2).
z is then projected into a higher dimensional space Z by Taken's delay
embedding for embedding dimension=2. So, the solution space is Z which is
a function of a's,b's. Minimization of Z will determine the actual value
of the parameters a,b.
Proposed Solution Approach - Based on any random initial value of Z, say
temp, taken from the solution space, I check how close temp is from the
current value curr of Z. Based on this result the next values of a and b
are taken and substituted into the equation of z(t).
Question - How do I apply Simulated Annealing for this problem? How do I
select the values of a and b depending on Z? I just cannot figure out the
code and the flow.
I have theoretical knowledge about SA and went through certain examples
presented in Matlab site but those are applicable when there is an
analytical form of the function. I do not know how I can apply for my
case. Please help.