Convergence of a hybrid projection-proximal point algorithm coupled with approximation methods in convex optimization

Felipe Alvarez, Miguel Carrasco, Karine Pichard

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

In order to minimize a closed convex function that is approximated by a sequence of better behaved functions, we investigate the global convergence of a general hybrid iterative algorithm, which consists of an inexact relaxed proximal point step followed by a suitable orthogonal projection onto a hyperplane. The latter permits to consider a fixed relative error criterion for the proximal step. We provide various sets of conditions ensuring the global convergence of this algorithm. The analysis is valid for nonsmooth data in infinite-dimensional Hilbert spaces. Some examples are presented, focusing on penalty/barrier methods in convex programming. We also show that some results can be adapted to the zero-finding problem for a maximal monotone operator.

Original languageEnglish
Pages (from-to)966-984
Number of pages19
JournalMathematics of Operations Research
Volume30
Issue number4
DOIs
StatePublished - Nov 2005
Externally publishedYes

Keywords

  • Diagonal iteration
  • Global convergence
  • Hybrid method
  • Parametric approximation
  • Proximal point

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