Parameter Optimization for Equilibrium Solutions of Mass Action Systems

University essay from Lunds universitet/Matematik LTH

Abstract: In this thesis, functions describing relations between chemical concentrations at equilibrium are studied. The functions have some parameters that are desired to be determined. Based on the properties of the functions, an optimization method will be proposed. Because of these special properties, it is appropriate to consider the residuals in the max norm, since then it is possible to show that there are only global minima. The existence of only global minima was proven by developing a theorem about preservation of strict quasiconvexity under the max operator. An algorithm is presented that finds a minimum in the max norm. The performance of this algorithm is compared to the performance of other algorithms. Primarily it is compared to optimization in the least square sense, since the least square norm is assumed to be better suited for the noise that is likely to be added to the points when making measurements. It was found that the proposed max norm algorithm worked well for the functions, but when the number of parameters and the deviation of the data points increased, the results were not satisfactory.

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