Projected subgradient methods with non-Euclidean distances for non-differentiable convex minimization and variational inequalities

Alfred Auslender, Marc Teboulle*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

We study subgradient projection type methods for solving non-differentiable convex minimization problems and monotone variational inequalities. The methods can be viewed as a natural extension of subgradient projection type algorithms, and are based on using non-Euclidean projection-like maps, which generate interior trajectories. The resulting algorithms are easy to implement and rely on a single projection per iteration. We prove several convergence results and establish rate of convergence estimates under various and mild assumptions on the problem's data and the corresponding step-sizes.

Original languageEnglish
Pages (from-to)27-48
Number of pages22
JournalMathematical Programming
Volume120
Issue number1 SPEC. ISS.
DOIs
StatePublished - Aug 2009

Keywords

  • Ergodic convergence
  • Interior projection-like maps
  • Non-differentiable convex optimization
  • Subgradient methods
  • Variational inequalities

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