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 Linearized Alternating Direction Method of Multipliers for Separable Convex Optimization of Real Functions in Complex Domain Lu Li,Lun Wang,Guoqiang Wang,Na Li,Juli Zhang Keywords:Linearized alternating direction method of multipliers, Variational Inequality, Wirtinger Calculus, Least absolute shrinkage and selectionator operator Abstract: The alternating direction method of multipliers (ADMM) for separable convex optimization of real functions in complex variables has been proposed recently\cite{LILU}. Furthermore, the convergence and $O(1/K)$ convergence rate of ADMM in complex domain have also been derived\cite{L.LiANZIAM}. In this paper, a fast linearized ADMM in complex domain has been presented as the subproblems do not have closed solutions. First, some useful results in complex domain are developed by using the Wirtinger Calculus technique. Second, the convergence of the linearized ADMM in complex domain based on the VI is established. Third, an extended model of least absolute shrinkage and selectionator operator (LASSO) is solved by using linearized ADMM in complex domain. Finally, some numerical simulations are provided to show that linearized ADMM in complex domain has the rapid speed.