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Dual decomposition methods are the current stateof-the-art for training multiclass formulations of Support Vector Machines (SVMs). At every iteration, dual decomposition methods update a small subset of dual variables by solving a restricted optimization problem. In this paper, we propose an exact and efficient method for solving the restricted problem. In our method, the restricted problem is reduced to the wellknown problem of Euclidean projection onto the positive simplex, which we can solvedoi:10.1109/icpr.2014.231 dblp:conf/icpr/BlondelFU14 fatcat:2cm5n5fdrvdm7jkf6rykbxc3zq