Acceleration of the PDHGM on Partially Strongly Convex Functions

Tuomo Valkonen*, Thomas Pock

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


We propose several variants of the primal–dual method due to Chambolle and Pock. Without requiring full strong convexity of the objective functions, our methods are accelerated on subspaces with strong convexity. This yields mixed rates, O(1 / N2) with respect to initialisation and O(1 / N) with respect to the dual sequence, and the residual part of the primal sequence. We demonstrate the efficacy of the proposed methods on image processing problems lacking strong convexity, such as total generalised variation denoising and total variation deblurring.

Original languageEnglish
Pages (from-to)394-414
Number of pages21
JournalJournal of Mathematical Imaging and Vision
Issue number3
Publication statusPublished - 1 Nov 2017


  • Accelerated
  • Primal–dual
  • Subspace
  • Total generalised variation

ASJC Scopus subject areas

  • Statistics and Probability
  • Modelling and Simulation
  • Condensed Matter Physics
  • Computer Vision and Pattern Recognition
  • Geometry and Topology
  • Applied Mathematics


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