Stochastic Primal-Dual Hybrid Gradient Algorithm with Arbitrary Sampling and Imaging Applications

Antonin Chambolle, Matthias J. Ehrhardt, Peter Richtárik, Carola-Bibiane Schönlieb

Research output: Contribution to journalArticlepeer-review

88 Citations (SciVal)


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.

Original languageEnglish
Pages (from-to)2783-2808
Number of pages26
JournalSIAM Journal on Optimization
Issue number4
Early online date2 Oct 2018
Publication statusPublished - 31 Dec 2018


  • Convex optimization
  • Imaging
  • Primal-dual algorithms
  • Saddle point problems
  • Stochastic optimization

ASJC Scopus subject areas

  • Software
  • Theoretical Computer Science


Dive into the research topics of 'Stochastic Primal-Dual Hybrid Gradient Algorithm with Arbitrary Sampling and Imaging Applications'. Together they form a unique fingerprint.

Cite this