Theoretical aspects of adopting exact penalty elements within sequential methods for nonlinear programming
Ademir A. Ribeiro(ademir.ribeiroufpr.br)
Abstract: 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.
Keywords: nonlinear programming; exact penalty function; smooth reformulation; feasibility; KKT conditions; Mangasarian-Fromovitz constraint qualiﬁcation.
Category 1: Nonlinear Optimization (Constrained Nonlinear Optimization )
Entry Submitted: 07/18/2013
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