Mathematical Programming

, Volume 125, Issue 1, pp 139–162 | Cite as

Global minimization using an Augmented Lagrangian method with variable lower-level constraints

Full length paper Series A

Abstract

A novel global optimization method based on an Augmented Lagrangian framework is introduced for continuous constrained nonlinear optimization problems. At each outer iteration k the method requires the \({\varepsilon_{k}}\) -global minimization of the Augmented Lagrangian with simple constraints, where \({\varepsilon_k \to \varepsilon}\) . Global convergence to an \({\varepsilon}\) -global minimizer of the original problem is proved. The subproblems are solved using the αBB method. Numerical experiments are presented.

Keywords

Deterministic global optimization Augmented Lagrangians Nonlinear programming Algorithms Numerical experiments 

Mathematics Subject Classification (2000)

90C30 65K05 

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Copyright information

© Springer-Verlag 2009

Authors and Affiliations

  • E. G. Birgin
    • 1
  • C. A. Floudas
    • 2
  • J. M. Martínez
    • 3
  1. 1.Department of Computer Science IME-USPUniversity of São PauloSão PauloBrazil
  2. 2.Department of Chemical EngineeringPrinceton UniversityPrincetonUSA
  3. 3.Department of Applied MathematicsIMECC-UNICAMP, University of CampinasCampinasBrazil

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