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

Ademir A. Ribeiro(ademir.ribeiro***at***ufpr.br)
Mael Sachine(mael***at***ufpr.br)
Sandra A. Santos(sandra***at***ime.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 )


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Entry Submitted: 07/18/2013
Entry Accepted: 07/18/2013
Entry Last Modified: 07/18/2013

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