Inertial proximal alternating linearized minimization (iPALM) for nonconvex and nonsmooth problems

Thomas Pock, Shoham Sabach

Research output: Contribution to journalArticlepeer-review


In this paper we study nonconvex and nonsmooth optimization problems with semialgebraic data, where the variables vector is split into several blocks of variables. The problem consists of one smooth function of the entire variables vector and the sum of nonsmooth functions for each block separately. We analyze an inertial version of the proximal alternating linearized minimization algorithm and prove its global convergence to a critical point of the objective function at hand. We illustrate our theoretical findings by presenting numerical experiments on blind image deconvolution, on sparse nonnegative matrix factorization and on dictionary learning, which demonstrate the viability and effectiveness of the proposed method.

Original languageEnglish
Pages (from-to)1756-1787
Number of pages32
JournalSIAM Journal on Imaging Sciences
Issue number4
Publication statusPublished - 2016


  • Alternating minimization
  • Blind image deconvolution
  • Block coordinate descent
  • Dictionary learning
  • Heavy ball method
  • Kurdyka-Łojasiewicz property
  • Nonconvex and nonsmooth minimization
  • Sparse nonnegative matrix factorization

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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