Summary: ``Dictionary-aided unmixing has been introduced as a semi-supervised unmixing method, under the assumption that the observed mixed pixel of a hyperspectral image can be expressed in the form of different linear combinations of a few spectral signatures from an available spectral library. Sparse-regression-based unmixing methods have been recently proposed to solve this problem. Mostly, $l_p$-norm minimization is a closer surrogate to the $l_0$-norm minimization and can be solved more efficiently than $l_1$-norm minimization. In this paper, we model the hyperspectral unmixing as a constrained $l_{2,q}-l_{2,p}$ optimization problem. To effectively solve the induced optimization problems for any $q$ $(1\leq q\leq2)$ and $p$ $(0