Abstract. In content-based image retrieval (CBIR) and image screening, it is often desirable to locate the regions of interest (ROI) in the images automatically. This can be accomplished with multi-instance learning techniques by treating each image as a bag of instances (regions). Many SVM-based methods are successful in predicting the bag labels, however, few of them can locate the ROIs. Moreover, they are often based on either local search or an EM-style strategy, and may get stuck in local minima easily. In this paper, we propose two convex optimization methods which maximize the margin of concepts via key instance generation at the instance-level and bag-level, respectively. Our formulation can be solved efficiently with a cutting plane algorithm. Experiments show that the proposed methods can effectively locate ROIs, and they also achieve performances competitive with state-of-the-art algorithms on benchmark data sets.