We propose a convex optimization approach for multi-label feature selection. The effective feature subset can be obtained through finding a global optima of a convex objective function for multi-label feature selection. However conventional greedy approaches are prone to suboptimal result. In this paper, the mathematical procedures and considerations for the optimization approach are presented for multi-label feature selection based on mutual information. We compared the proposed method with conventional greedy search based methods to show the potential of optimization based multi-label feature selection.