Augmented Lagrangians

  • Alexander Rubinov
  • Xiaoqi Yang
Part of the Applied Optimization book series (APOP, volume 85)


In the previous chapters we have studied duality relations by using Lagrange-type function. A different approach is based on the notion of a dualizing parameterization function and the corresponding augmented Lagrangian that is an augmented (nonlinear) version of the classical linear Lagrange function. An augmented Lagrangian, which is generated by the so-called canonical dualizing parameterization, can also be considered as a Lagrange-type function corresponding to a certain convolution function. However, augmented Lagrangians using a general dualizing parameterization function cannot be derived using convolution functions.


Dual Problem Dual Function Lower Semicontinuous Function Perturbation Function Weak Duality 
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Copyright information

© Springer Science+Business Media Dordrecht 2003

Authors and Affiliations

  • Alexander Rubinov
    • 1
  • Xiaoqi Yang
    • 2
  1. 1.School of Information Technology and Mathematical SciencesUniversity of BallaratVictoriaAustralia
  2. 2.Department of Applied MathematicsHong Kong Polytechnic UniversityHong KongChina

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