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In this paper, we extend the implementable APG method to solve the matrix l 2,1 -norm minimization problem arising in multi-task feature learning. We investigate that the resulting inner subproblem has closed-form solution which can be easily determined by taking the problem's favorable structures. Under suitable conditions, we can establish a comprehensive convergence result for the proposed method. Furthermore, we present three different inexact APG algorithms by using the Lipschitz constant,doi:10.19139/106 fatcat:ubpp2fgznvd47cseux3syl3lfi