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

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989100%3A27240%2F14%3A86092153" target="_blank" >RIV/61989100:27240/14:86092153 - isvavai.cz</a>
Alternative codes found
RIV/61989100:27740/14:86092153
Result on the web
<a href="http://download.springer.com/static/pdf/914/art%253A10.1007%252Fs10589-013-9611-2.pdf?auth66=1426149691_115cfecb6fa36396f89c61c83a43e0bd&ext=.pdf" target="_blank" >http://download.springer.com/static/pdf/914/art%253A10.1007%252Fs10589-013-9611-2.pdf?auth66=1426149691_115cfecb6fa36396f89c61c83a43e0bd&ext=.pdf</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s10589-013-9611-2" target="_blank" >10.1007/s10589-013-9611-2</a>

Result language
angličtina
Original language name
On R-linear convergence of semi-monotonic inexact augmented Lagrangians for saddle point problems
Original language 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 usesa 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
Czech name
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Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Project
Result was created during the realization of more than one project. More information in the Projects tab.
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>Z - Vyzkumny zamer (s odkazem do CEZ)

Publication year
2014
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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