ON THE TWICE DIFFERENTIABLE CUBIC AUGMENTED LAGRANGIAN

Rockafellar's quadratic augmented Lagrangian for inequality constraine d 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 Bregman-related Lagrangia ns.