AUC is widely used as a measure for the imbalanced classification problems. The AUC loss problem is a pairwise function between two instances from different classes, which is obviously different from that in standard binary classifications. How to improve its real convergence speed is an interesting problem. Recent study shows that the online method (OAM) using the reservoir sampling technique has better performance. However, there exist some shortcomings such as slow convergence rate and difficult parameter selection. This paper conducts a systematic investigation for solving AUC optimization problem by using the dual coordinate descent methods (AUC-DCD). It presents three kinds of algorithms: AUC-SDCD, AUC-SDCDperm and AUC-MSGD, where the first two algorithms depend on the size of training set while the last does not. Theoretical analysis shows that OAM is a special case of the AUC-DCD. Experimental results show that AUC-DCD is better than OAM on the AUC performance as well as the convergence rate. Therefore AUC-DCD is among the first optimization schemes suggested for efficiently solving AUC problems.