On the \(O(1/K)\) convergence rate of alternating direction method of multipliers in a complex domain

We focus on the convergence rate of the alternating direction method of multipliers (ADMM) in a complex domain. First, the complex form of variational inequality (VI) is established by using the Wirtinger calculus technique. Second, the \(O(1/K)\) convergence rate of the ADMM in a complex domain is provided. Third, the ADMM in a complex domain is applied to the least absolute shrinkage and selectionator operator (LASSO). Finally, numerical simulations are provided to show that ADMM in a complex domain has the \(O(1/K)\) convergence rate and that it has certain advantages compared with the ADMM in a real domain. doi:10.1017/S1446181118000184