On the \(O(1/K)\) convergence rate of alternating direction method of multipliers in a complex domain
DOI:
https://doi.org/10.21914/anziamj.v60i0.11945Keywords:
the alternating direction method of multipliers, convergence rate, Wirtinger calculus, least absolute shrinkage and selectionator operator.Abstract
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/S1446181118000184Published
2018-10-07
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