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

Lu Li, G. Q. Wang, J. L. Zhang

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/S1446181118000184

Keywords


the alternating direction method of multipliers, convergence rate, Wirtinger calculus, least absolute shrinkage and selectionator operator.



DOI: http://dx.doi.org/10.21914/anziamj.v60i0.11945



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