Journal of Global Optimization

, Volume 40, Issue 4, pp 545–573 | Cite as

A geometric framework for nonconvex optimization duality using augmented lagrangian functions

Original Paper

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.

Keywords

Augmented Lagrangian functions Duality Penalty 

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Copyright information

© Springer Science+Business Media, Inc. 2006

Authors and Affiliations

  1. 1.Department of Industrial and Enterprise Systems EngineeringUniversity of IllinoisUrbanaUSA
  2. 2.Department of Electrical Engineering and Computer ScienceMassachusetts Institute of TechnologyCambridgeUSA

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