An extended linearized alternating direction method of multipliers for Fused-LASSO penalized linear regression

In terms of variable selection and dimensionality reduction for high-dimensional data, Fused-LASSO is a powerful model when the number of important variables is small and neighboring variables exhibit a high degree of correlation. However, solving the model is challenging due to its non-smoothness and non-separability. Alternating direction method of multipliers (ADMM) is an effective method to solve the Fused-LASSO, but one of the subproblems may have no closed-form solution leading to additional computational overhead, and the computing for the inverse of matrix in the subproblem is expensive. In order to overcome these shortcomings and have a great speed performance, an extended linearized alternating direction method of multipliers (ELADMM) is proposed in this paper. First, in the framework of ADMM, we embed the linearized technique into the x-subproblem, so that the subproblem can be solved quickly and efficiently rather than by inner iteration. Second, we make additional extensions to some variables after each iteration, which improves the speed performance of the LADMM. Numerical results show that the proposed ELADMM outperforms ADMM as well as other existing solvers in the sense that it finds the same accurate variable selection results with the shortest time.