The estimation of abundance maps in hyperspectral imaging requires the resolution of an optimization problem under nonnegativity and sum to one constraints. Assuming that the spectral signatures of the image components have been previously determined by an endmember extraction algorithm, we propose here a primal-dual interior point algorithm for the estimation of their fractional abundances. In comparison with the reference method FCLS, our algorithm has the advantage of a reduced computational cost, especially in the context of large scale images and allows to deal with a penalized criterion favoring the spatial smoothness of abundance maps. The performances of the proposed approach are discussed with the help of synthetic and real examples.