Convexification procedures and decomposition methods for nonconvex optimization problems

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59 Scopus citations

Abstract

In order for primal-dual methods to be applicable to a constrained minimization problem, it is necessary that restrictive convexity conditions are satisfied. In this paper, we consider a procedure by means of which a nonconvex problem is convexified and transformed into one which can be solved with the aid of primal-dual methods. Under this transformation, separability of the type necessary for application of decomposition algorithms is preserved. This feature extends the range of applicability of such algorithms to nonconvex problems. Relations with multiplier methods are explored with the aid of a local version of the notion of a conjugate convex function.

Original languageEnglish (US)
Pages (from-to)169-197
Number of pages29
JournalJournal of Optimization Theory and Applications
Volume29
Issue number2
DOIs
StatePublished - Oct 1979
Externally publishedYes

Keywords

  • Primal-dual methods
  • convexification procedures
  • decomposition methods
  • local convex conjugate functions
  • multiplier methods

ASJC Scopus subject areas

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

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