A simplified view of first order methods for optimization

Marc Teboulle*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


We discuss the foundational role of the proximal framework in the development and analysis of some iconic first order optimization algorithms, with a focus on non-Euclidean proximal distances of Bregman type, which are central to the analysis of many other fundamental first order minimization relatives. We stress simplification and unification by highlighting self-contained elementary proof-patterns to obtain convergence rate and global convergence both in the convex and the nonconvex settings, which in turn also allows to present some novel results.

Original languageEnglish
Pages (from-to)67-96
Number of pages30
JournalMathematical Programming
Issue number1
StatePublished - 1 Jul 2018


  • Convex and nonconvex minimization
  • Descent Lemma
  • First order algorithms
  • Kurdyka–Łosiajewicz property
  • Non-Euclidean Bregman distance
  • Proximal framework


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