A geometric framework for nonconvex optimization duality using augmented lagrangian functions

Angelia Nedich, Asuman Ozdaglar

Research output: Contribution to journalArticle

18 Citations (Scopus)

Abstract

We provide a unifying geometric framework for the analysis of general classes of duality schemes and penalty methods for nonconvex constrained optimization problems. We present a separation result for nonconvex sets via general concave surfaces. We use this separation result to provide necessary and sufficient conditions for establishing strong duality between geometric primal and dual problems. Using the primal function of a constrained optimization problem, we apply our results both in the analysis of duality schemes constructed using augmented Lagrangian functions, and in establishing necessary and sufficient conditions for the convergence of penalty methods.

Original languageEnglish (US)
Pages (from-to)545-573
Number of pages29
JournalJournal of Global Optimization
Volume40
Issue number4
DOIs
StatePublished - Apr 2008
Externally publishedYes

Fingerprint

Augmented Lagrangian Function
Nonconvex Optimization
Constrained optimization
Duality
Penalty Method
Constrained Optimization Problem
Necessary Conditions
Strong Duality
Sufficient Conditions
Dual Problem
Framework
analysis
method
penalty
Optimization problem
Penalty method

Keywords

  • Augmented Lagrangian functions
  • Duality
  • Penalty

ASJC Scopus subject areas

  • Applied Mathematics
  • Control and Optimization
  • Management Science and Operations Research
  • Global and Planetary Change

Cite this

A geometric framework for nonconvex optimization duality using augmented lagrangian functions. / Nedich, Angelia; Ozdaglar, Asuman.

In: Journal of Global Optimization, Vol. 40, No. 4, 04.2008, p. 545-573.

Research output: Contribution to journalArticle

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