- Theoretical aspects of adopting exact penalty elements within sequential methods for nonlinear programming Ademir A. Ribeiro(ademir.ribeiroufpr.br) Mael Sachine(maelufpr.br) Sandra A. Santos(sandraime.unicamp.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 ) Citation: Download: [PDF]Entry Submitted: 07/18/2013Entry Accepted: 07/18/2013Entry Last Modified: 07/18/2013Modify/Update this entry Visitors Authors More about us Links Subscribe, Unsubscribe Digest Archive Search, Browse the Repository Submit Update Policies Coordinator's Board Classification Scheme Credits Give us feedback Optimization Journals, Sites, Societies Optimization Online is supported by the Mathematical Optmization Society.