This article considers the decomposition of a nonnegative signal into a non-negative linear combination of the contributions of pre-specified atomic units, which are also nonnegative. This model, referred as compositional model, is evident in the time-frequency characterisations of audio signals, where the sound can be viewed as a blending of spectral patterns of the component sounds that are present simultaneously. The algorithm proposed in this article obtains the activation vector of the atoms through an Active-Set Newton algorithm that employ the Alpha-Beta-divergence between the observed signal and the decomposition. This divergence family has been proved to be more efficient than other more common divergences, such as the generic Kullback-Leibler divergence in various audio signal processing applications. We have evaluated the proposed algorithm in a signal separation application of polyphonic music.