minimization over contraction -help needed

Hi,

I have a code that works at two levels. In the first level, it finds a vector of values (call it V) and a vector of actions (i.e. a vector of numbers; let us call the vector S) that satisfies the Bellman equation via contraction:

V=B*max{E[A+V']}

where V' denotes the value at next period, E[.] is the expectation operator. The state transitions are Markov, transition probabilities are determined by S and are constant over time.At this level I have no issues.

At the second level, the code tries to find a set of parameter values to equate a weighted squared sum of the elements of S to an empirically observed value (a scalar). The weights are calculated as the ergodic state distribution of the Markov chain and hence depend on S as well.

To do so I define a function handle to minimize the absolute difference between the empirical value and the weighted sum mentioned above, then run fminunc or fminsearch to find the parameters to minimize the sum. However, with both functions I get the initial values as the optimal values in the end -and yes, I did try many different initial values; the result was always the same. I also tried to tweak the parameters TolFun and TolX but they only served to increase the runtime.

I would be grateful if someone could tell what I may be doing wrong here and even more so if you could suggest how I can overcome this issue.

If further clarification is needed, just let me know.

Cheers,

Baran