An Augmented Lagrangian Function with Improved Exactness Properties

In this paper we introduce a new exact augmented Lagrangian function for the solution of general nonlinear programming problems. For this Lagrangian function a complete equivalence between its unconstrained minimization on an open set and the solution of the original constrained problem can be established under mild assumptions and without requiring the boundedness of the feasible set of the constrained problem. Moreover we describe an unconstrained algorithmic model which is globally convergent toward KKT pairs of the original constrained problem. The algorithmic model can be endowed with a superlinear rate of convergence by a proper choice of the search direction in the unconstrained minimization, without requiring strict complementarity.

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