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On the twice differentiable cubic augmented Lagrangian

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Abstract

Rockafellar's quadratic augmented Lagrangian for inequality constrained minimization is not twice differentiable. To eliminate this drawback, several quite complicated Lagrangians have been proposed. We exhibit a simple cubic Lagrangian that is twice differentiable. It stems from the recent work of Eckstein and Teboulle on Bregmanrelated Lagrangians.

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Authors and Affiliations

  1. Systems Research Institute, Warsaw, Poland

    K. C. Kiwiel (Associate Professor)

Authors
  1. K. C. Kiwiel
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Additional information

Communicated by O. L. Mangasarian

This research was supported by the State Committee for Scientific Research under Grant 8S50502206.

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Kiwiel, K.C. On the twice differentiable cubic augmented Lagrangian. J Optim Theory Appl 88, 233–236 (1996). https://doi.org/10.1007/BF02192031

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  • DOI: https://doi.org/10.1007/BF02192031

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