Addressing the greediness phenomenon in Nonlinear Programming by means of Proximal Augmented Lagrangians

Abstract

When one solves Nonlinear Programming problems by means of algorithms that use merit criteria combining the objective function and penalty feasibility terms, a phenomenon called greediness may occur. Unconstrained minimizers attract the iterates at early stages of the calculations and, so, the penalty parameter needs to grow excessively, in such a way that ill-conditioning harms the overall convergence. In this paper a regularization approach is suggested to overcome this difficulty. An Augmented Lagrangian method is defined with the addition of a regularization term that inhibits the possibility that the iterates go far from a reference point. Convergence proofs and numerical examples are given.