Extended monotropic programming and duality

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19 Scopus citations

Abstract

We consider the problem min Σi=1m f i(xi) s.t. x ε S, where xi are multidimensional subvectors of x, fi are convex functions, and S is a subspace. Monotropic programming, extensively studied by Rockafellar, is the special case where the subvectors xi are the scalar components of x. We show a strong duality result that parallels Rockafellar's result for monotropic programming, and contains other known and new results as special cases. The proof is based on the use of ε-subdifferentials and the ε-descent method, which is used here as an analytical vehicle.

Original languageEnglish (US)
Pages (from-to)209-225
Number of pages17
JournalJournal of Optimization Theory and Applications
Volume139
Issue number2
DOIs
StatePublished - Nov 2008
Externally publishedYes

Keywords

  • Duality
  • Monotropic
  • ε-descent
  • ε-subdifferential

ASJC Scopus subject areas

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

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