This is indeed a challenging problem. I worked on a related optics problem involving MEMS a while back, and found that it was crucial to have a model of the problem so that the optimizer would not spend a ton of time futilely optimizing while in the wrong basin of attraction. What I mean is, it is very helpful if you have some idea of reasonable settings before you start to optimize so that you are not going into a local optimum that is not good.
However, if the measurements are fast and you are willing to invest a lot of cycles in optimizing for a given setup, you can just use patternsearch starting from a large variety of initial settings. Set the bounds to [-1,1] in every component, and fire away, something like this:
ub = ones(40,1);
lb = -ub;
options = psoptimset('InitialMeshSize',1/4); % or some such thing
x0 = lb + rand(size(lb)).*(ub - lb); % you will do this many times
voltages = patternsearch(yourfun,x0,[],[],[],[],lb,ub,[],options);
Good luck,
Alan Weiss
MATLAB mathematical toolbox documentation
