Abstract
The quadratic penalty function is widely used in the practical implementations of methods of multipliers. There is a tangible advantage in using a different penalty function. The objective function is bounded below along the constraint set and the augmented Lagrangian is unbounded over the entire space for every value of the penalty parameter. The augmented Lagrangian functions for inequality constraints and some of the approximating functions do not have continuous second derivatives. The methods to be used for unconstrained minimization of the augmented Lagrangian rely on the continuity of second derivatives. Multiplier methods corresponding to different types of penalty functions can exhibit different rates of convergence.
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