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Augmented Lagrangian methods for nonlinear programming with possible infeasibility

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Abstract

In this paper, we consider a nonlinear programming problem for which the constraint set may be infeasible. We propose an algorithm based on a large family of augmented Lagrangian functions and analyze its global convergence properties taking into account the possible infeasibility of the problem. We show that, in a finite number of iterations, the algorithm stops detecting the infeasibility of the problem or finds an approximate feasible/optimal solution with any required precision. We illustrate, by means of numerical experiments, that our algorithm is reliable for different Lagrangian/penalty functions proposed in the literature.

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Acknowledgments

This work was supported in part by Projeto 136/11- CAPES/MES-Cuba, CNPq Grant 471815/2012-8 and 444134/2014-0, and FAPEG/GO.

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Correspondence to L. F. Prudente.

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Gonçalves, M.L.N., Melo, J.G. & Prudente, L.F. Augmented Lagrangian methods for nonlinear programming with possible infeasibility. J Glob Optim 63, 297–318 (2015). https://doi.org/10.1007/s10898-015-0289-0

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