Constrained nonnegative matrix factorization was an excellent method for hyperspectral unmixing.The traditional algorithm of this method was based on projected gradient method

and its convergence rate

accuracy and stability needed to be improved.To this end

we considered the excellent minimum volume constraint

and proposed a fast algorithm for hyperspectral unmixing based on constrained nonnegative matrix factorization.First the minimum volume constrained model of the original problem was optimized

then an alternating direction method of multipliers was used to solve the non-convex constrained nonnegative matrix factorization

and at last we modified the iteration steps by singular value decomposition.Experimental results on simulated and real hyperspectral data demonstrate the superiority of the proposed algorithm.