The boundedness of penalty parameters in an augmented Lagrangian method with constrained subproblems

Augmented Lagrangian methods are effective tools for solving large-scale nonlinear programming problems. At each outer iteration, a minimization subproblem with simple constraints, whose objective function depends on updated Lagrange multipliers and penalty parameters, is approximately solved. When...

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Vydáno v:	Optimization methods & software Ročník 27; číslo 6; s. 1001 - 1024
Hlavní autoři:	Birgin, Ernesto G., Fernández, Damián, Martínez, J. M.
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	Abingdon Taylor & Francis 01.12.2012 Taylor & Francis Ltd
Témata:	Algorithms augmented Lagrangian methods Computer programs Fines & penalties Lagrange multipliers Mathematical analysis Mathematical models Nonlinear programming numerical experiments Optimization penalty parameters Software Studies
ISSN:	1055-6788, 1029-4937
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Abstract	Augmented Lagrangian methods are effective tools for solving large-scale nonlinear programming problems. At each outer iteration, a minimization subproblem with simple constraints, whose objective function depends on updated Lagrange multipliers and penalty parameters, is approximately solved. When the penalty parameter becomes very large, solving the subproblem becomes difficult; therefore, the effectiveness of this approach is associated with the boundedness of the penalty parameters. In this paper, it is proved that under more natural assumptions than the ones employed until now, penalty parameters are bounded. For proving the new boundedness result, the original algorithm has been slightly modified. Numerical consequences of the modifications are discussed and computational experiments are presented.
AbstractList	Augmented Lagrangian methods are effective tools for solving large-scale nonlinear programming problems. At each outer iteration, a minimization subproblem with simple constraints, whose objective function depends on updated Lagrange multipliers and penalty parameters, is approximately solved. When the penalty parameter becomes very large, solving the subproblem becomes difficult; therefore, the effectiveness of this approach is associated with the boundedness of the penalty parameters. In this paper, it is proved that under more natural assumptions than the ones employed until now, penalty parameters are bounded. For proving the new boundedness result, the original algorithm has been slightly modified. Numerical consequences of the modifications are discussed and computational experiments are presented. [PUBLICATION ABSTRACT] Augmented Lagrangian methods are effective tools for solving large-scale nonlinear programming problems. At each outer iteration, a minimization subproblem with simple constraints, whose objective function depends on updated Lagrange multipliers and penalty parameters, is approximately solved. When the penalty parameter becomes very large, solving the subproblem becomes difficult; therefore, the effectiveness of this approach is associated with the boundedness of the penalty parameters. In this paper, it is proved that under more natural assumptions than the ones employed until now, penalty parameters are bounded. For proving the new boundedness result, the original algorithm has been slightly modified. Numerical consequences of the modifications are discussed and computational experiments are presented.
Author	Birgin, Ernesto G. Fernández, Damián Martínez, J. M.
Author_xml	– sequence: 1 givenname: Ernesto G. surname: Birgin fullname: Birgin, Ernesto G. email: egbirgin@ime.usp.br organization: Department of Computer Science , Institute of Mathematics and Statistics, University of São Paulo – sequence: 2 givenname: Damián surname: Fernández fullname: Fernández, Damián organization: Department of Applied Mathematics , Institute of Mathematics, Statistics and Scientific Computing, University of Campinas – sequence: 3 givenname: J. M. surname: Martínez fullname: Martínez, J. M. organization: Department of Applied Mathematics , Institute of Mathematics, Statistics and Scientific Computing, University of Campinas
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Cites_doi	10.1023/A:1018665102534 10.1007/BFb0121177 10.1002/jcc.10216 10.1093/imanum/6.3.357 10.1007/s10589-007-9050-z 10.1007/s101070100263 10.1016/0022-247X(67)90163-1 10.1007/s10107-009-0264-y 10.1007/s10107-002-0364-4 10.1023/A:1019928808826 10.1007/s10898-009-9419-x 10.1007/s10589-009-9240-y 10.1007/s10589-007-9159-0 10.1007/s10589-005-1066-7 10.1023/A:1022686919295 10.1137/1.9780898719857 10.1080/10556780802124648 10.1137/060667086 10.1080/02331930500100270 10.1007/BFb0120989 10.1007/s101070050051 10.1007/BF00927673 10.1137/S1052623497326629 10.1007/BF01580138 10.1137/060654797 10.1002/jcc.21224 10.1007/s10107-004-0559-y 10.1007/s10957-004-1861-9
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SubjectTerms	Algorithms augmented Lagrangian methods Computer programs Fines & penalties Lagrange multipliers Mathematical analysis Mathematical models Nonlinear programming numerical experiments Optimization penalty parameters Software Studies
Title	The boundedness of penalty parameters in an augmented Lagrangian method with constrained subproblems
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