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ON THE
$O(1/K)$ CONVERGENCE RATE OF THE ALTERNATING DIRECTION METHOD OF MULTIPLIERS IN A COMPLEX DOMAIN
- Part of
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- Journal:
- The ANZIAM Journal / Volume 60 / Issue 1 / July 2018
- Published online by Cambridge University Press:
- 30 August 2018, pp. 95-117
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- Article
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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.
