Abstract
The alternating direction method of multipliers (ADMM) is applied to a constrained linear least-squares problem, where the objective function is a sum of two least-squares terms and there are box constraints. The original problem is decomposed into two easier least-squares subproblems at each iteration, and to speed up the inner iteration we linearize the relevant subproblem whenever it has no known closed-form solution. We prove the convergence of the resulting algorithm, and apply it to solve some image deblurring problems. Its efficiency is demonstrated, in comparison with Newton-type methods.
| Original language | English |
|---|---|
| Pages (from-to) | 326-341 |
| Number of pages | 16 |
| Journal | East Asian Journal on Applied Mathematics |
| Volume | 2 |
| Issue number | 4 |
| DOIs | |
| Publication status | Published - Nov 2012 |
| Externally published | Yes |
Funding
Our research is supported in part by HKRGC Grant No. CUHK400510 and the CUHK Direct Allocation Grant 2060408, the Scientific Research Foundation of the Nanjing University of Posts and Telecommunications (NY210049), and the Hong Kong General Research Fund: HKBU 203311.
Keywords
- Alternating direction method of multipliers
- Image processing
- Linear least-squares problems
- Linearization