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Statements

Subject Item
n2:RIV%2F61989100%3A27740%2F14%3A86092153%21RIV15-MSM-27740___
rdf:type
skos:Concept n20:Vysledek
rdfs:seeAlso
http://download.springer.com/static/pdf/914/art%253A10.1007%252Fs10589-013-9611-2.pdf?auth66=1426149691_115cfecb6fa36396f89c61c83a43e0bd&ext=.pdf
dcterms: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
dcterms: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
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
skos:notation
RIV/61989100:27740/14:86092153!RIV15-MSM-27740___
n3:aktivita
n14:Z n14:P
n3:aktivity
P(ED1.1.00/02.0070), P(GP101/09/P601), Z(MSM6198910027)
n3:cisloPeriodika
1
n3:dodaniDat
n10:2015
n3:domaciTvurceVysledku
n16:5021391 n16:7610173
n3:druhVysledku
n17:J
n3:duvernostUdaju
n12:S
n3:entitaPredkladatele
n9:predkladatel
n3:idSjednocenehoVysledku
34364
n3:idVysledku
RIV/61989100:27740/14:86092153
n3:jazykVysledku
n15:eng
n3:klicovaSlova
Periodic boundary conditions; Error bounds; Adaptive precision control; Augmented Lagrangians; Equality constraints; s Quadratic programming
n3:klicoveSlovo
n8:Augmented%20Lagrangians n8:Adaptive%20precision%20control n8:Equality%20constraints n8:s%20Quadratic%20programming n8:Error%20bounds n8:Periodic%20boundary%20conditions
n3:kodStatuVydavatele
US - Spojené státy americké
n3:kontrolniKodProRIV
[8437C9DFD1E7]
n3:nazevZdroje
Computational Optimization and Applications
n3:obor
n4:BA
n3:pocetDomacichTvurcuVysledku
2
n3:pocetTvurcuVysledku
3
n3:projekt
n13:ED1.1.00%2F02.0070 n13:GP101%2F09%2FP601
n3:rokUplatneniVysledku
n10:2014
n3:svazekPeriodika
58
n3:tvurceVysledku
Vodstrčil, Petr Dostál, Zdeněk Horák, David
n3:wos
000334524000003
n3:zamer
n18:MSM6198910027
s:issn
0926-6003
s:numberOfPages
17
n11:doi
10.1007/s10589-013-9611-2
n21:organizacniJednotka
27740