This paper reports on a novel model based on convex optimization methods for the analysis of the skin conductance (SC) as response of the electrodermal activity (EDA) to affective stimuli. Starting from previous assessed methodological approaches, this new model proposes a decomposition of SC into tonic and phasic components through the solution of a convex optimization problem. Previous knowledge about the physiology of the EDA is accounted for by means of an appropriate choice of constraints and regularizers. In order to test the effectiveness of the new approach, an experimental session in which 9 healthy subjects were stimulated using affective pictures gathered from the IAPS database was designed and carried out. The experimental session included series of negative-valence high-arousal images and series of neutral images, with an inter-stimulus interval of about 2 seconds for both neutral and high arousal pictures. Next, a statistical analysis was performed on a set of features extracted from the phasic driver and the tonic signal estimated by the model. Results showed that the phasic driver extracted from the model was able to strongly distinguish arousal sessions from neutral ones. Conversely, no significant difference was found for the tonic components. This experimental findings are consistent with the literature and confirm that the phasic component is strictly related to changes in the sympathetic activity of the autonomic nervous system. Although preliminary, these results are very encouraging and future work will progress to further validate the model through specific and controlled experiments.