Linearly-Convergent FISTA Variant for Composite Optimization with Duality

Casey Garner, Shuzhong Zhang

Research output: Contribution to journalArticlepeer-review


Many large-scale optimization problems can be expressed as composite optimization models. Accelerated first-order methods such as the fast iterative shrinkage–thresholding algorithm (FISTA) have proven effective for numerous large composite models. In this paper, we present a new variation of FISTA, to be called C-FISTA, which obtains global linear convergence for a broader class of composite models than many of the latest FISTA variants. We demonstrate the versatility and effectiveness of C-FISTA through multiple numerical experiments on group Lasso, group logistic regression and geometric programming models. Furthermore, we utilize Fenchel duality to show C-FISTA can solve the dual of a finite sum convex optimization model.

Original languageEnglish (US)
Article number65
JournalJournal of Scientific Computing
Issue number3
StatePublished - Mar 2023

Bibliographical note

Funding Information:
This material is based upon work supported by the National Science Foundation Graduate Research Fellowship Program under Grant No. 1839286. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.

Publisher Copyright:
© 2023, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.


  • Accelerated first-order algorithm
  • Composite optimization
  • Fenchel duality
  • Group Lasso


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