Coupling the proximal point algorithm with approximation methods

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Abstract

We study the convergence of a diagonal process for minimizing a closed proper convex function f, in which a proximal point iteration is applied to a sequence of functions approximating f. We prove that, when the approximation is sufficiently fast, and also when it is sufficiently slow, the sequence generated by the method converges toward a minimizer of f. Comparison to previous work is provided through examples in penalty methods for linear programming and Tikhonov regularization.

Original languageEnglish
Pages (from-to)581-600
Number of pages20
JournalJournal of Optimization Theory and Applications
Volume95
Issue number3
DOIs
StatePublished - Dec 1997

Keywords

  • Convex optimization
  • Penalty methods
  • Proximal point algorithm
  • Steepest descent
  • Viscosity methods

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