About: On R-linear convergence of semi-monotonic inexact augmented Lagrangians for saddle point problems

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About: On R-linear convergence of semi-monotonic inexact augmented Lagrangians for saddle point problems Goto Sponge NotDistinct Permalink

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rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
rdfs:seeAlso	http://download.springer.com/static/pdf/914/art%253A10.1007%252Fs10589-013-9611-2.pdf?auth66=1426149691_115cfecb6fa36396f89c61c83a43e0bd&ext=.pdf
Description	A variant of the inexact augmented Lagrangian algorithm called SMALE (Dostál in Comput. Optim. Appl. 38:47–59, 2007) for the solution of saddle point problems with a positive definite left upper block is studied. The algorithm SMALEM presented here uses a fixed regularization parameter and controls the precision of the solution of auxiliary unconstrained problems by a multiple of the norm of the residual of the second block equation and a constant which is updated in order to enforce increase of the Lagrangian function. A nice feature of SMALE-M inherited from SMALE is its capability to find an approximate solution in a number of iterations that is bounded in terms of the extreme eigenvalues of the left upper block and does not depend on the off-diagonal blocks. Here we prove the R-linear rate of convergence of the outer loop of SMALE-M for any regularization parameter. The theory is illustrated by numerical experiments A variant of the inexact augmented Lagrangian algorithm called SMALE (Dostál in Comput. Optim. Appl. 38:47–59, 2007) for the solution of saddle point problems with a positive definite left upper block is studied. The algorithm SMALEM presented here uses a fixed regularization parameter and controls the precision of the solution of auxiliary unconstrained problems by a multiple of the norm of the residual of the second block equation and a constant which is updated in order to enforce increase of the Lagrangian function. A nice feature of SMALE-M inherited from SMALE is its capability to find an approximate solution in a number of iterations that is bounded in terms of the extreme eigenvalues of the left upper block and does not depend on the off-diagonal blocks. Here we prove the R-linear rate of convergence of the outer loop of SMALE-M for any regularization parameter. The theory is illustrated by numerical experiments (en)
Title	On R-linear convergence of semi-monotonic inexact augmented Lagrangians for saddle point problems On R-linear convergence of semi-monotonic inexact augmented Lagrangians for saddle point problems (en)
skos:prefLabel	On R-linear convergence of semi-monotonic inexact augmented Lagrangians for saddle point problems On R-linear convergence of semi-monotonic inexact augmented Lagrangians for saddle point problems (en)
skos:notation	RIV/61989100:27740/14:86092153!RIV15-MSM-27740___
http://linked.open...avai/riv/aktivita	P Z
http://linked.open...avai/riv/aktivity	P(ED1.1.00/02.0070), P(GP101/09/P601), Z(MSM6198910027)
http://linked.open...iv/cisloPeriodika	1
http://linked.open...vai/riv/dodaniDat	2015
http://linked.open...aciTvurceVysledku	Dostál, Zdeněk Horák, David
http://linked.open.../riv/druhVysledku	J - Článek v odborném periodiku
http://linked.open...iv/duvernostUdaju	S - Úplné a pravdivé údaje nepodléhající ochraně podle zvláštních právních předpisů
http://linked.open...titaPredkladatele	Vysoká škola báňská - Technická univerzita Ostrava / IT4Innovations
http://linked.open...dnocenehoVysledku	34364
http://linked.open...ai/riv/idVysledku	RIV/61989100:27740/14:86092153
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	Periodic boundary conditions; Error bounds; Adaptive precision control; Augmented Lagrangians; Equality constraints; s Quadratic programming (en)
http://linked.open.../riv/klicoveSlovo	Periodic boundary conditions Error bounds Adaptive precision control Augmented Lagrangians s Quadratic programming Equality constraints
http://linked.open...odStatuVydavatele	US - Spojené státy americké
http://linked.open...ontrolniKodProRIV	[8437C9DFD1E7]
http://linked.open...i/riv/nazevZdroje	Computational Optimization and Applications
http://linked.open...in/vavai/riv/obor	BA
http://linked.open...ichTvurcuVysledku	2 (xsd:int)
http://linked.open...cetTvurcuVysledku	3 (xsd:int)
http://linked.open...vavai/riv/projekt	Adaptation of scalable FETI based algorithms for the solution of large scale 3D elasticity engineering problems with large number of bodies in contact IT4Innovations Centre of Excellence
http://linked.open...UplatneniVysledku	2014
http://linked.open...v/svazekPeriodika	58
http://linked.open...iv/tvurceVysledku	Dostál, Zdeněk Horák, David Vodstrčil, Petr
http://linked.open...ain/vavai/riv/wos	000334524000003
http://linked.open...n/vavai/riv/zamer	Výpočetně náročné počítačové simulace a optimalizace
issn	0926-6003
number of pages	17 (xsd:int)
http://bibframe.org/vocab/doi	10.1007/s10589-013-9611-2
http://localhost/t...ganizacniJednotka	27740

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