Abstract: A multi-Lagrange multiplier support vector machine fast training method (MLSVM) based on the coordinated optimization of multi-Lagrange multipliers is proposed and the formula to define the feasible field of each multiplier is presented. The algorithm approaches to the most optimization more precisely and quickly due to the analytic expressions adopted in the optimization process of each multiplier. The SMO algorithm is proved to be an instance of MLSVM. Three individual lgorithms, i.e., MLSVM1, MLSVM2 and MLSVM3, are presented under the theoretical guidance of this method according to different learning strategies. The learning speed of MLSVM1 and MLSVM2 is about the same as that of SMO when the test data set is small (＜5000). However, they will fail when the test data set becomes larger. MLSVM3 is an improved algorithm of the former two algorithms and the SMO algorithm. It not only overcomes the failure of MLSVM1 and MLSVM2, but also performs faster than the SMO algorithm with an improvement of 7.4% to 4130% on several test data sets.