Theoretical aspects of adopting exact penalty elements within sequential methods for nonlinear programming

In the context of sequential methods for solving general nonlinear programming problems, it is usual to work with augmented subproblems instead of the original ones, tackled by the $\ell_1$-penalty function together with the shortcut usage of a convenient penalty parameter. This paper addresses the theoretical reasoning behind handling the original subproblems by such an augmentation strategy, by means of the differentiable reformulation of the $\ell_1$-penalized problem. The convergence properties of related sequences of problems are analyzed. Furthermore, examples that elucidate the interrelations among the obtained results are presented.