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Augmented Lagrangian methods under the constant positive linear dependence constraint qualification

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Abstract

Two Augmented Lagrangian algorithms for solving KKT systems are introduced. The algorithms differ in the way in which penalty parameters are updated. Possibly infeasible accumulation points are characterized. It is proved that feasible limit points that satisfy the Constant Positive Linear Dependence constraint qualification are KKT solutions. Boundedness of the penalty parameters is proved under suitable assumptions. Numerical experiments are presented.

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Authors and Affiliations

  1. Department of Applied Mathematics, IMECC-UNICAMP, University of Campinas, CP 6065, 13081-970, Campinas, SP, Brazil

    R. Andreani, J. M. Martínez & M. L. Schuverdt

  2. Department of Computer Science IME-USP, University of São Paulo, Rua do Matão 1010, Cidade Universitária, 05508-090, São Paulo, SP, Brazil

    E. G. Birgin

Authors
  1. R. Andreani
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  2. E. G. Birgin
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  3. J. M. Martínez
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  4. M. L. Schuverdt
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Correspondence to E. G. Birgin.

Additional information

Dedicated to Clovis Gonzaga on the occassion of his 60th birthday.

The authors were supported by PRONEX - CNPq / FAPERJ E-26 / 171.164/2003 - APQ1, FAPESP (Grants 2001/04597-4, 2002/00094-0, 2003/09169-6, 2002/00832-1 and 2005/56773-1) and CNPq.

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Andreani, R., Birgin, E.G., Martínez, J.M. et al. Augmented Lagrangian methods under the constant positive linear dependence constraint qualification. Math. Program. 111, 5–32 (2008). https://doi.org/10.1007/s10107-006-0077-1

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  • DOI: https://doi.org/10.1007/s10107-006-0077-1

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