Coupling general penalty schemes for convex programming with the steepest descent and the proximal point algorithm

R. Cominetti, M. Courdurier

Research output: Contribution to journalArticlepeer-review

22 Scopus citations

Abstract

We study the asymptotic behavior of the continuous flow generated by coupling the steepest descent method with a general class of penalty schemes for convex programming. We establish convergence of the trajectories towards primal optimal solutions, as well as convergence of some naturally associated dual paths. The results are extended to the sequences generated by an implicit discretization scheme which corresponds to the coupling of an inexact proximal point iteration with the penalty schemes.

Original languageEnglish
Pages (from-to)745-765
Number of pages21
JournalSIAM Journal on Optimization
Volume13
Issue number3
DOIs
StatePublished - 2003

Keywords

  • Convex programming
  • Penalty schemes
  • Prox method
  • Subgradient inclusions

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