Convergence of an inexact majorization-minimization method for solving a class of composite optimization problems

Amir Beck, Dror Pan

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review

Abstract

We suggest a majorization-minimization method for solving nonconvex minimization problems. The method is based on minimizing at each iterate a properly constructed consistent majorizer of the objective function. We describe a variety of classes of functions for which such a construction is possible. We introduce an inexact variant of the method, in which only approximate minimization of the consistent majorizer is performed at each iteration. Both the exact and the inexact algorithms are shown to be descent methods whose accumulation points have a property which is stronger than standard stationarity. We give examples of cases in which the exact method can be applied. Finally, we show that the inexact method can be applied to a specific problem, called sparse source localization, by utilizing a fast optimization method on a smooth convex dual of its subproblems.

Original languageEnglish
Title of host publicationLecture Notes in Mathematics
PublisherSpringer Verlag
Pages375-410
Number of pages36
DOIs
StatePublished - 2018

Publication series

NameLecture Notes in Mathematics
Volume2227
ISSN (Print)0075-8434

Keywords

  • Composite model
  • Majorization minimization
  • Nonconvex programming

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