A truncated Newton method in an augmented Lagrangian framework for nonlinear programming
In this paper we propose a primal-dual algorithm for the solution of general nonlinear programming problems. The core of the method is a local algorithm which relies on a truncated procedure for the computation of a search direction, and is thus suitable for large scale problems. The truncated direc...
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| Vydané v: | Computational optimization and applications Ročník 45; číslo 2; s. 311 - 352 |
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| Hlavní autori: | , , , |
| Médium: | Journal Article |
| Jazyk: | English |
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01.03.2010
Springer Nature B.V |
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| ISSN: | 0926-6003, 1573-2894 |
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| Abstract | In this paper we propose a primal-dual algorithm for the solution of general nonlinear programming problems. The core of the method is a local algorithm which relies on a truncated procedure for the computation of a search direction, and is thus suitable for large scale problems. The truncated direction produces a sequence of points which locally converges to a KKT pair with superlinear convergence rate.
The local algorithm is globalized by means of a suitable merit function which is able to measure and to enforce progress of the iterates towards a KKT pair, without deteriorating the local efficiency. In particular, we adopt the exact augmented Lagrangian function introduced in Pillo and Lucidi (SIAM J. Optim. 12:376–406,
2001
), which allows us to guarantee the boundedness of the sequence produced by the algorithm and which has strong connections with the above mentioned truncated direction.
The resulting overall algorithm is globally and superlinearly convergent under mild assumptions. |
|---|---|
| AbstractList | In this paper we propose a primal-dual algorithm for the solution of general nonlinear programming problems. The core of the method is a local algorithm which relies on a truncated procedure for the computation of a search direction, and is thus suitable for large scale problems. The truncated direction produces a sequence of points which locally converges to a KKT pair with superlinear convergence rate. The local algorithm is globalized by means of a suitable merit function which is able to measure and to enforce progress of the iterates towards a KKT pair, without deteriorating the local efficiency. In particular, we adopt the exact augmented Lagrangian function introduced in Pillo and Lucidi (SIAM J. Optim. 12:376-406, 2001), which allows us to guarantee the boundedness of the sequence produced by the algorithm and which has strong connections with the above mentioned truncated direction. The resulting overall algorithm is globally and superlinearly convergent under mild assumptions.[PUBLICATION ABSTRACT] In this paper we propose a primal-dual algorithm for the solution of general nonlinear programming problems. The core of the method is a local algorithm which relies on a truncated procedure for the computation of a search direction, and is thus suitable for large scale problems. The truncated direction produces a sequence of points which locally converges to a KKT pair with superlinear convergence rate. The local algorithm is globalized by means of a suitable merit function which is able to measure and to enforce progress of the iterates towards a KKT pair, without deteriorating the local efficiency. In particular, we adopt the exact augmented Lagrangian function introduced in Pillo and Lucidi (SIAM J. Optim. 12:376-406, 2001), which allows us to guarantee the boundedness of the sequence produced by the algorithm and which has strong connections with the above mentioned truncated direction. The resulting overall algorithm is globally and superlinearly convergent under mild assumptions. In this paper we propose a primal-dual algorithm for the solution of general nonlinear programming problems. The core of the method is a local algorithm which relies on a truncated procedure for the computation of a search direction, and is thus suitable for large scale problems. The truncated direction produces a sequence of points which locally converges to a KKT pair with superlinear convergence rate. The local algorithm is globalized by means of a suitable merit function which is able to measure and to enforce progress of the iterates towards a KKT pair, without deteriorating the local efficiency. In particular, we adopt the exact augmented Lagrangian function introduced in Pillo and Lucidi (SIAM J. Optim. 12:376–406, 2001 ), which allows us to guarantee the boundedness of the sequence produced by the algorithm and which has strong connections with the above mentioned truncated direction. The resulting overall algorithm is globally and superlinearly convergent under mild assumptions. |
| Author | Di Pillo, Gianni Palagi, Laura Lucidi, Stefano Liuzzi, Giampaolo |
| Author_xml | – sequence: 1 givenname: Gianni surname: Di Pillo fullname: Di Pillo, Gianni email: dipillo@dis.uniroma1.it organization: Dipartimento di Informatica e Sistemistica “Antonio Ruberti”, Università di Roma “La Sapienza” – sequence: 2 givenname: Giampaolo surname: Liuzzi fullname: Liuzzi, Giampaolo organization: CNR–Consiglio Nazionale delle Ricerche, IASI–Istituto di Analisi dei Sistemi ed Informatica “A. Ruberti” – sequence: 3 givenname: Stefano surname: Lucidi fullname: Lucidi, Stefano organization: Dipartimento di Informatica e Sistemistica “Antonio Ruberti”, Università di Roma “La Sapienza” – sequence: 4 givenname: Laura surname: Palagi fullname: Palagi, Laura organization: Dipartimento di Informatica e Sistemistica “Antonio Ruberti”, Università di Roma “La Sapienza” |
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| Cites_doi | 10.1007/BF01581275 10.1007/978-3-663-12160-2 10.1007/BF02192227 10.1137/S1052623497321894 10.1007/s101070100263 10.1007/PL00011391 10.1007/BF00940345 10.1145/962437.962439 10.1137/0327068 10.1023/A:1008677427361 10.1137/S1052623496305560 10.1007/BF02591986 10.1137/0802027 10.1137/S1052623499357258 10.1016/0167-6377(94)00059-F 10.1007/BF01588240 10.1137/0724076 10.1137/S1052623497325107 10.1007/s101070100244 10.1007/BF01385810 |
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| Keywords | Large scale optimization Exact augmented Lagrangian functions Truncated Newton-type algorithms Nonlinear programming algorithms Constrained optimization |
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| References_xml | – reference: QiL.SunJ.A nonsmooth version of Newton’s methodMath. Program.19935835336710.1007/BF015812751216791 – reference: Di PilloG.GrippoL.An exact penalty method with global convergence propertiesMath. Program.19863611810.1007/BF02591986 – reference: GladT.PolakE.A multiplier method with automatic limitation of penalty growthMath. Program.1979171401550414.9007810.1007/BF01588240546352 – reference: OrthegaJ.M.RheinboldtW.C.Iterative Solution of Nonlinear Equations in Several Variables1970San DiegoAcademic Press – reference: YabeH.YamashitaH.Superlinear and quadratic convergence of some primal-dual interior point methods for constrained optimizationMath. Program.1996753773971422177 – reference: Di PilloG.GrippoL.Toft-ChristensenE.A class of continuously differentiable exact penalty function algorithms for nonlinear programming problemsSystem Modelling and Optimization1984BerlinSpringer – reference: Di PilloG.GrippoL.Exact penalty functions in constrained optimizationSIAM J. Control Optim.198927133313600681.4903510.1137/03270681022431 – reference: GrippoL.LamparielloF.LucidiS.A truncated Newton method with nonmonotone line search for unconstrained optimizationJ. Optim. Theory Appl.1989604014190632.9005910.1007/BF00940345993007 – reference: ShannoD.F.VanderbeiR.J.An interior point algorithm for nonconvex nonlinear programmingComput. Optim. Appl.1999132312521040.9056410.1023/A:10086774273611704122 – reference: ByrdR.H.HribarM.E.NocedalJ.An interior point algorithm for large-scale nonlinear programmingSIAM J. 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| SubjectTerms | Algorithms Convex and Discrete Geometry Globalization Lagrange multiplier Management Science Mathematics Mathematics and Statistics Nonlinear programming Operations Research Operations Research/Decision Theory Optimization Optimization techniques Statistics Studies |
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| Title | A truncated Newton method in an augmented Lagrangian framework for nonlinear programming |
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