A recent trend in exemplar based unsupervised learning is to formulate the learning problem as a convex optimization problem. Convexity is achieved by restricting the set of possible prototypes to training exemplars. In particular, this has been done for clustering, vector quantization and mixture model density estimation. In this paper we propose a novel algorithm that is theoretically and practically superior to these convex formulations. This is possible by posing the unsupervised learning problem as a single convex "master problem" with non-convex subproblems. We show that for the above learning tasks the subproblems are extremely well-behaved and can be solved efficiently.