Dykstra's algorithm as the nonlinear extension of Bregman's optimization method

Lev M. Bregman, Yair Censor, Simeon Reich

Research output: Contribution to journalArticlepeer-review


We show that Dykstra's algorithm with Bregman projections, which finds the Bregman projection of a point onto the nonempty intersection of finitely many closed convex sets, is actually the nonlinear extension of Bregman's primal-dual, dual coordinate ascent, row-action minimization algorithm. Based on this observation we give an alternative convergence analysis and a new geometric interpretation of Dykstra's algorithm with Bregman projections which complements recent work of Censor and Reich, Bauschke and Lewis, and Tseng.

Original languageEnglish
Pages (from-to)319-333
Number of pages15
JournalJournal of Convex Analysis
Issue number2
StatePublished - 1999


  • Bregman projection
  • Convex programming
  • Dykstra's algorithm

ASJC Scopus subject areas

  • Analysis
  • Mathematics (all)


Dive into the research topics of 'Dykstra's algorithm as the nonlinear extension of Bregman's optimization method'. Together they form a unique fingerprint.

Cite this