Existing feature selection methods typically do not consider prior knowledge in the form of structural relationships among features. In this study, the features are structured based on prior knowledge into groups. The problem addressed in this article is how to select one representative feature from each group such that the selected features are jointly discriminating the classes. The problem is formulated as a binary constrained optimization and the combinatorial optimization is relaxed as a convex-concave problem, which is then transformed into a sequence of convex optimization problems so that the problem can be solved by any standard optimization algorithm. Moreover, a block coordinate gradient descent optimization algorithm is proposed for high dimensional feature selection, which in our experiments was four times faster than using a standard optimization algorithm.