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

Thomas Pock, Shoham Sabach

Research output: Contribution to journalArticle

Abstract

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.

LanguageEnglish
Pages1756-1787
Number of pages32
JournalSIAM Journal on Imaging Sciences
Volume9
Issue number4
DOIs
StatusPublished - 2016

Fingerprint

Nonsmooth Function
Non-negative Matrix Factorization
Nonsmooth Optimization
Nonconvex Optimization
Deconvolution
Sparse matrix
Glossaries
Factorization
Viability
Global Convergence
Smooth function
Critical point
Objective function
Numerical Experiment
Entire
Optimization Problem
Demonstrate
Experiments
Learning
Dictionary

Keywords

  • 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

Cite this

Inertial proximal alternating linearized minimization (iPALM) for nonconvex and nonsmooth problems. / Pock, Thomas; Sabach, Shoham.

In: SIAM Journal on Imaging Sciences, Vol. 9, No. 4, 2016, p. 1756-1787.

Research output: Contribution to journalArticle

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