This paper studies estimation algorithms for nonlinear hyperspectral image unmixing. The proposed unmixing model assumes that the pixel reflectances are polynomial functions of linear mixtures of pure spectral components contaminated by an additive white Gaussian noise. A hierarchical Bayesian algorithm and an optimization method are proposed for solving the resulting unmixing problem. The parameters involved in the proposed model satisfy constraints that are naturally included in the estimation procedure. The performance of the unmixing strategies is evaluated thanks to simulations conducted on synthetic and real data.