Abstract In this paper, we formulate a sparse optimization framework for extractive document summarization. The proposed framework has a decomposable convex objective function. We derive an efficient ADMM algorithm to solve it. To encourage diversity in the summaries, we explicitly introduce an additional sentence dissimilarity term in the optimization framework. We achieve significant improvement over previous related work under similar data reconstruction framework. We then generalize our formulation to the case of compressive summarization and derive a block coordinate descent algorithm to optimize the objective function. Performance on DUC 2006 and DUC 2007 datasets shows that our compressive summarization results are competitive against the state-of-the-art results while maintaining reasonable readability.