SIAM Journal on Imaging Sciences· 2012Q1
Convergence Analysis of Primal-Dual Algorithms for a Saddle-Point Problem: From Contraction Perspective
- 388citations
- Q1SCImago
- 2012year
Short summary
New primal-dual algorithms for saddle-point problems, applicable to image restoration, allow for significantly larger parameters (like step sizes) when simple correction steps are added, leading to contraction-type convergence.
AI-generated from the title and abstract; the full text is not read.
Key points
- New primal-dual algorithms are proposed for saddle-point problems, with applications in image restoration.
- Simple correction steps allow for significantly enlarged parameters (e.g., step sizes) in these algorithms.
- The new methods are shown to be of the contraction type, generating contractive iterative sequences.
- This contraction perspective simplifies convergence analysis and guarantees global convergence.
AI-generated from the title and abstract; the full text is not read.
Abstract
Recently, some primal-dual algorithms have been proposed for solving a saddle-point problem, with particular applications in the area of total variation image restoration. This paper focuses on the convergence analysis of these primal-dual algorithms and shows that their involved parameters (including step sizes) can be significantly enlarged if some simple correction steps are supplemented. Some new primal-dual–based methods are thus proposed for solving the saddle-point problem. We show that these new methods are of the contraction type: the iterative sequences generated by these new methods are contractive with respect to the solution set of the saddle-point problem. The global convergence of these new methods thus can be obtained within the analytic framework of contraction-type methods. The novel study on these primal-dual algorithms from the perspective of contraction methods substantially simplifies existing convergence analysis. Finally, we show the efficiency of the new methods numerically.
The authors' abstract, as published at the source. SIAM Journal on Imaging Sciences, 2012 · DOI ↗
Continue with a free account
Ask the paper: 3 free questions a day about this paper; save it, get its citation, new summaries every day for your field. Takeaways are Premium.
Continue free on the webSign in with Google or Apple; no card needed. You come back to this paper.
On your phone:
Field: Mathematical Physics
Mathematical PhysicsMathematics