EURO Journal on Computational Optimization

, Volume 4, Issue 1, pp 27–46 | Cite as

On the rate of convergence of the proximal alternating linearized minimization algorithm for convex problems

  • Ron Shefi
  • Marc TeboulleEmail author
Original Paper


We analyze the proximal alternating linearized minimization algorithm (PALM) for solving non-smooth convex minimization problems where the objective function is a sum of a smooth convex function and block separable non-smooth extended real-valued convex functions. We prove a global non-asymptotic sublinear rate of convergence for PALM. When the number of blocks is two, and the smooth coupling function is quadratic we present a fast version of PALM which is proven to share a global sublinear rate efficiency estimate improved by a squared root factor. Some numerical examples illustrate the potential benefits of the proposed schemes.


Non-smooth convex minimization Alternating proximal methods Coordinate descent Non-asymptotic rate of convergence 

Mathematics Subject Classification

90C25 49M27 65K05 


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Copyright information

© EURO - The Association of European Operational Research Societies 2015

Authors and Affiliations

  1. 1.School of Mathematical SciencesTel-Aviv UniversityRamat-AvivIsrael

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