| Volume 14, Number 6, 2024, Pages - DOI：10.11948/JAAC-2023-0407 |
| Convergence analysis on the alternating direction method of multipliers for the cosparse optimization problem |
| Zisheng Liu,Ting Zhang |
| Keywords:sparse representation model, cosparse analysis model, alternating direction method of multipliers, variational inequality, convergence analysis |
| Abstract: |
| From a dual perspective of the sparse representation model, Nam et al. proposed the cosparse analysis model. In this paper, we aim to investigate the convergence of the alternating direction method of multipliers (ADMM) for the cosparse optimization problem. First, we examine the variational inequality representation of the cosparse optimization problem by introducing auxiliary variables. Second, ADMM is used to solve cosparse optimization problem. Finally, by utilizing a tight frame with a uniform row norm and building upon lemmas and the strict contraction theorem, we establish a worst-case $\mathcal{O}(1/t)$ convergence rate in the ergodic sense. The experimental results verify the practicability and convergence of the ADMM in solving cosparse optimization problems. |
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