On the twice differentiable cubic augmented Lagrangian

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