It doesn't look like your Lag is much of a constant if there's 4000 values for it. Does Lag changes with R (since there's also 4000 R values)?
You can use fminsearch or fminbnd but if there's only 4000 values for R and 11 for alpha, you could simply calculate the result for all of them at once and get the minimum :
[R, alpha] = ndgrid(1:4000, 1:0.1:2); %get all combinations of R and alpha
result = Nug + Sill * (1 - exp(-bsxfun(@rdivide, Lag, R) .^ alpha)); %assumes Lag is a column vector with 4000 elements
[minvalue, location] = min(result(:));
minR = R(location)
minalpha = alpha(location)
