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

Authors

  • Lu Li Shanghai University of Engineering Science
  • G. Q. Wang Shanghai University of Engineering Science
  • J. L. Zhang Shanghai University of Engineering Science

DOI:

https://doi.org/10.21914/anziamj.v60i0.11945

Keywords:

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/S1446181118000184

Author Biographies

Lu Li, Shanghai University of Engineering Science

School of Mathematics, Physics and Statistics, Shanghai University of Engineering Science, Shanghai.

G. Q. Wang, Shanghai University of Engineering Science

School of Mathematics, Physics and Statistics, Shanghai University of Engineering Science, Shanghai.

J. L. Zhang, Shanghai University of Engineering Science

School of Mathematics, Physics and Statistics, Shanghai University of Engineering Science, Shanghai.

Published

2018-10-07

Issue

Section

Articles for Printed Issues