STOCHASTIC PRIMAL-DUAL HYBRID GRADIENT ALGORITHM WITH ARBITRARY SAMPLING AND IMAGING APPLICATIONS

被引：102

作者：

Chambolle, Antonin ^{[1
]}

Ehrhardt, Matthias J. ^{[2
]}

Richtarik, Peter ^{[3
,4
,5
,6
]}

Schonlieb, Carola-Bibiane ^{[2
]}

机构：

[1] Ecole Polytech, CNRS, CMAP, F-91128 Palaiseau, France

[2] Univ Cambridge, Dept Appl Math & Theoret Phys, Cambridge CB3 0WA, England

[3] KAUST, Visual Comp Ctr, Thuwal 23955, Saudi Arabia

[4] KAUST, Extreme Comp Res Ctr, Thuwal 23955, Saudi Arabia

[5] Univ Edinburgh, Sch Math, Edinburgh EH9 3PD, Midlothian, Scotland

[6] Alan Turing Inst, London NW1 2DB, England

来源：

SIAM JOURNAL ON OPTIMIZATION | 2018年 / 28卷 / 04期

基金：

英国工程与自然科学研究理事会; 欧盟地平线“2020”;

关键词：

convex optimization; primal-dual algorithms; saddle point problems; stochastic optimization; imaging; OPTIMIZATION; FRAMEWORK;

D O I：

10.1137/17M1134834

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We propose a stochastic extension of the primal-dual hybrid gradient algorithm studied by Chambolle and Pock in 2011 to solve saddle point problems that are separable in the dual variable. The analysis is carried out for general convex-concave saddle point problems and problems that are either partially smooth / strongly convex or fully smooth / strongly convex. We perform the analysis for arbitrary samplings of dual variables, and we obtain known deterministic results as a special case. Several variants of our stochastic method significantly outperform the deterministic variant on a variety of imaging tasks.

引用

页码：2783 / 2808

页数：26

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