A brief overview of nonparametric mixture model, constrained nonparametric mixture model, and interior point method is presented. We apply an interior point method to constrained nonparametric mixture models. This application is based on a Bender's decomposition of the mixture likelihood function. An advantage of the proposed method is that it can handle nonlinearities in the model as well as constraints on latent variables. Numerical results are presented along with comparisons to Gradient based method.