In this article, we address the problem of face recognition under uncontrolled conditions. The proposed solution is a numerical robust algorithm dealing with face images automatically registered and projected via the linear discriminant analysis (LDA) into a holistic low-dimensional feature space. At the heart of this discriminative system, there are suitable nonconvex parametric mappings based on which a fixed-point technique finds the sparse representation of test images allowing their classification. We theoretically argue that the success achieved in sparsity promoting is due to the sequence of values imposed on a characteristic parameter of the used mapping family. Experiments carried out on several databases (ORL, YaleB, BANCA, FRGC v2.0) show the robustness and the ability of the system for classification purpose. In particular, within the area of sparsity promotion, our recognition system shows very good performance with respect to those achieved by the state-of-the-art ℓ1 norm-based sparse representation classifier (SRC), the recently proposed ℓ2 norm-based collaborative representation classifier (CRC), the LASSO-based sparse decomposition technique, and the weighted sparse representation method (WSRC), which integrates sparsity and data locality structure.