Five areas where I have done this sort of thing come to mind:
1. Back in the days when it was considered desirable to have a water profile that matched a specified one for the style I would estimate the vector of salt additions that minimized mean square log concentration error between the realized log concentrations calculated from an addition vector and log concentrations in the profile. I did this first with simulated annealing and later with iterative Moore-Penrose. Now, when I do this which is rare, I use the Excel Solver.
2. The Tineseth bittering model has two parameters. I had a collection of beers on which I had measured IBU's and used iterative Moore-Penrose to find the values of the two parameters that minimized the rmse IBU prediction error RE the measured values.
3. In estimating mash pH the answer is the pH at which the proton deficits for all basic substances just balance the proton surfeits of the acidic substances (or, allowing that an acid has a negative proton deficit, the pH at which the sum of all the proton deficits is 0). The individual mash component proton deficits are non linear functions of the trial pH. As the error is a scalar simple root bisection serves to find the solution (though I usually let Excel do it using whatever hairy gradient approach(es) it employs.
4. pH meter electrode produces voltage V = V0 -s*(R/F)*T*(pH - pHi). R and F are two constants and T the temperature in Kelvins. I have used iterative Moore-Penrose to jointly estimate the V0, s and pHi that minimize rmse between observed voltages and voltages predicted by the formula over a large number of measurements on two buffers (known pH) at different temperatures.
5. In a similar vein I tried to model the response of a sodium ISE in the non-Nernstian portion of its range (where my well's sodium content lies) by spiking samples. Can't say that one was a big success.
Though optimization was not involved I have eigencharacterized an ensemble of 99 beer absorption spectra (about 8000 spectral measurements) and determined that SRM alone accounts of about 92% of the variation between beer transmission spectra. I was also able to compute a couple (2, 3, 4) eignenvectors that characterize the rest.
