Majority of the image set based face recognition methods use a generatively learned model for each person that is learned independently by ignoring the other persons in the gallery set. In contrast to these methods, this paper introduces a novel method that searches for discriminative convex models that best fit to an individual's face images but at the same time are as far as possible from the images of other persons in the gallery. We learn discriminative convex models for both affine and convex hulls of image sets. During testing, distances from the query set images to these models are computed efficiently by using simple matrix multiplications, and the query set is assigned to the person in the gallery whose image set is closest to the query images. The proposed method significantly outperforms other methods using generative convex models in terms of both accuracy and testing time, and achieves the state-of-the-art results on three of the five tested datasets. Especially, the accuracy improvement is significant on the challenging PaSC, COX and ESOGU video datasets.