Several supervised, semi-supervised, and unsupervised machine learning schemes can be unified under the general framework of graph embedding. Incorporating graph embedding principles into sparse representation based learning schemes can provide an improved performance in several learning tasks. In this work, we propose a dictionary learning procedure for computing discriminative sparse codes that obey graph embedding constraints. In order to compute the graph-embedded sparse codes, we integrate a modified version of the sequential quadratic programming procedure with the feature sign search method. We demonstrate, using simulations with the AR face database, that the proposed approach performs better than several baseline methods in supervised and semi-supervised classification.