Augmented Lagrangian methods under the constant positive linear dependence constraint qualification

Authors:
R. Andreani;E. G. Birgin;J. M. Martínez;M. L. Schuverdt
Affiliations:
University of Campinas, Department of Applied Mathematics, IMECC-UNICAMP, CP 6065, 13081-970, Campinas, SP, Brazil;University of São Paulo, Department of Computer Science IME-USP, CP 6065, Rua do Matão 1010, Cidade Universitária, 05508-090, São Paulo, SP, Brazil;University of Campinas, Department of Applied Mathematics, IMECC-UNICAMP, CP 6065, 13081-970, Campinas, SP, Brazil;University of Campinas, Department of Applied Mathematics, IMECC-UNICAMP, CP 6065, 13081-970, Campinas, SP, Brazil
Venue:
Mathematical Programming: Series A and B
Year:
2007

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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.