Simultaneous parameter estimation and model structure determination in FTIR spectroscopy by global MINLP optimization

We address the problem of simultaneous model structure determination and parameter estimation in infrared spectroscopy. For given measurements of concentrations (C) and absorbances (A), we seek to find the constant of analogy (θ) in reverse Beer's law (C = θA). Two approaches are described and compared in this paper. Both utilize Akaike's information criterion (AIC) to obtain an estimate of the constant. The first method is frequently used in practice and requires the iterative solution of mixed-integer convex quadratic optimization problems. The second method is a novel one that requires the solution of a single mixed-integer nonconvex nonlinear program for which we develop a global optimization algorithm. Computational results demonstrate that the latter approach provides better solutions for all of the eleven problems solved in this paper. Our computational experiments also reveal the importance of bounding the errors and number of model parameters when minimizing AIC.