Auxiliary problem principle and decomposition of optimization problems

G. Cohen

Research output: Contribution to journalArticlepeer-review

302 Scopus citations

Abstract

The auxiliary problem principle allows one to find the solution of a problem (minimization problem, saddle-point problem, etc.) by solving a sequence of auxiliary problems. There is a wide range of possible choices for these problems, so that one can give special features to them in order to make them easier to solve. We introduced this principle in Ref. 1 and showed its relevance to decomposing a problem into subproblems and to coordinating the subproblems. Here, we derive several basic or abstract algorithms, already given in Ref. 1, and we study their convergence properties in the framework of i infinite-dimensional convex programming.

Original languageEnglish
Pages (from-to)277-305
Number of pages29
JournalJournal of Optimization Theory and Applications
Volume32
Issue number3
DOIs
StatePublished - 1 Nov 1980
Externally publishedYes

Keywords

  • Convex programming
  • coordination
  • decomposition
  • large-scale systems
  • optimization algorithms

ASJC Scopus subject areas

  • Control and Optimization
  • Management Science and Operations Research
  • Applied Mathematics

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