On a proximal point method for convex optimization in banach spaces

Dan Butnariu, Alfredo N. Iusem

Research output: Contribution to journalArticlepeer-review


We analyze the behavior of a parallel proximal point method for solving convex optimization problems in reflexive Banach spaces. Similar algorithms were known to converge under the implicit assumption that the norm of the space is Hilbertian. We extend the area of applicability of the proximal point method to solving convex optimization problems in Banach spaces on which totally convex functions can be found. This includes the class of all smooth uniformly convex Banach spaces. Also, our convergence results leave more flexibility for the choice of the penalty function involved in the algorithm and, in this way, allow simplification of the computational procedure.

Original languageEnglish
Pages (from-to)723-744
Number of pages22
JournalNumerical Functional Analysis and Optimization
Issue number7-8
StatePublished - 1997


  • Bochner integral
  • Bregman distance
  • Convex optimization problem
  • Proximal point method
  • Totally convex function
  • Uniformly convex Banach space

ASJC Scopus subject areas

  • Analysis
  • Signal Processing
  • Computer Science Applications
  • Control and Optimization


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