On the Convergence of Primal-Dual Hybrid Gradient Algorithm

The primal-dual hybrid gradient algorithm (PDHG) has been widely used, especially for some basic image processing models. In the literature, PDHG's convergence was established only under some restrictive conditions on its step sizes. In this paper, we revisit PDHG's convergence in the cont...

Celý popis

Uloženo v:
Podrobná bibliografie
Vydáno v:SIAM journal on imaging sciences Ročník 7; číslo 4; s. 2526 - 2537
Hlavní autoři: He, Bingsheng, You, Yanfei, Yuan, Xiaoming
Médium: Journal Article
Jazyk:angličtina
Vydáno: 01.01.2014
Témata:
Algorithms
Complexity
Constants
Convergence
Image processing
Imaging
Iterative methods
Mathematical models
ISSN:1936-4954, 1936-4954
On-line přístup:Získat plný text
Tagy: Přidat tag
Žádné tagy, Buďte první, kdo vytvoří štítek k tomuto záznamu!
Popis
Shrnutí:The primal-dual hybrid gradient algorithm (PDHG) has been widely used, especially for some basic image processing models. In the literature, PDHG's convergence was established only under some restrictive conditions on its step sizes. In this paper, we revisit PDHG's convergence in the context of a saddle-point problem and try to better understand how to choose its step sizes. More specifically, we show by an extremely simple example that PDHG is not necessarily convergent even when the step sizes are fixed as tiny constants. We then show that PDHG with constant step sizes is indeed convergent if one of the functions of the saddle-point problem is strongly convex, a condition that does hold for some variational models in imaging. With this additional condition, we also establish a worst-case convergence rate measured by the iteration complexity for PDHG with constant step sizes.
Bibliografie:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 23
ISSN:1936-4954
1936-4954
DOI:10.1137/140963467