Proximal decomposition via alternating linearization

Krzysztof C. Kiwiel, Charles H. Rosa, Andrzej Ruszczyński

Research output: Contribution to journalArticlepeer-review

37 Scopus citations

Abstract

A new approximate proximal point method for minimizing the sum of two convex functions is introduced. It replaces the original problem by a sequence of regularized subproblem in which the functions are alternately represented by linear models. The method updates the linear models and the prox center, as well as the prox coefficient. It is monotone in terms of the objective values and converges to a solution of the problem, if any. A dual version of the method is derived and analyzed Applications of the methods to multistage stochastic programming problems are discussed and preliminary numerical experience is presented.

Original languageEnglish (US)
Pages (from-to)668-689
Number of pages22
JournalSIAM Journal on Optimization
Volume9
Issue number3
DOIs
StatePublished - Jan 1 1999

All Science Journal Classification (ASJC) codes

  • Software
  • Theoretical Computer Science

Keywords

  • Augmented Lagrangians
  • Convex programming
  • Decomposition
  • Large scale optimization
  • Proximal point methods
  • Stochastic programming

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