Recent advances of experimental techniques in biology have led to the production of enormous amounts of data on the dynamics of genetic regulatory networks. We present an approach for the identification of PieceWise-Affine (PWA) models of genetic regulatory networks from experimental data, focusing on the reconstruction of switching thresholds associated with regulatory interactions. In particular, our method takes into account geometric constraints specific to models of genetic regulatory networks. We show the feasibility of our approach by the reconstruction of switching thresholds in a PWA model of the carbon starvation response in the bacterium Escherichia coli.