A new fast method to compute saddle-points in constrained optimization and applications
| hal.structure.identifier | Laboratoire d'Analyse, Topologie, Probabilités [LATP] | |
| dc.contributor.author | ANGOT, Philippe | |
| hal.structure.identifier | Transferts, écoulements, fluides, énergétique [TREFLE] | |
| dc.contributor.author | CALTAGIRONE, Jean-Paul | |
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | FABRIE, Pierre | |
| dc.date.accessioned | 2024-04-04T02:26:40Z | |
| dc.date.available | 2024-04-04T02:26:40Z | |
| dc.date.created | 2011-01-01 | |
| dc.date.issued | 2012 | |
| dc.identifier.issn | 0893-9659 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/189970 | |
| dc.description.abstractEn | The solution of the augmented Lagrangian related system $(A+r\,B^TB)\,\rv=f$ is a key ingredient of many iterative algorithms for the solution of saddle-point problems in constrained optimization with quasi-Newton methods. However, such problems are ill-conditioned when the penalty parameter $\eps=1/r>0$ tends to zero, whereas the error vanishes as $\cO(\eps)$. We present a new fast method based on a {\em splitting penalty scheme} to solve such problems with a judicious prediction-correction. We prove that, due to the {\em adapted right-hand side}, the solution of the correction step only requires the approximation of operators independent on $\eps$, when $\eps$ is taken sufficiently small. Hence, the proposed method is all the cheaper as $\eps$ tends to zero. We apply the two-step scheme to efficiently solve the saddle-point problem with a penalty method. Indeed, that fully justifies the interest of the {\em vector penalty-projection methods} recently proposed in \cite{ACF08} to solve the unsteady incompressible Navier-Stokes equations, for which we give the stability result and some quasi-optimal error estimates. Moreover, the numerical experiments confirm both the theoretical analysis and the efficiency of the proposed method which produces a fast splitting solution to augmented Lagrangian or penalty problems, possibly used as a suitable preconditioner to the fully coupled system. | |
| dc.language.iso | en | |
| dc.publisher | Elsevier | |
| dc.subject.en | Constrained optimization | |
| dc.subject.en | Saddle-point problems | |
| dc.subject.en | Augmented Lagrangian | |
| dc.subject.en | Penalty method | |
| dc.subject.en | Splitting prediction-correction scheme | |
| dc.subject.en | Vector penalty-projection methods | |
| dc.title.en | A new fast method to compute saddle-points in constrained optimization and applications | |
| dc.type | Article de revue | |
| dc.identifier.doi | 10.1016/j.aml.2011.08.015 | |
| dc.subject.hal | Mathématiques [math]/Optimisation et contrôle [math.OC] | |
| dc.subject.hal | Mathématiques [math]/Analyse numérique [math.NA] | |
| dc.subject.hal | Mathématiques [math]/Equations aux dérivées partielles [math.AP] | |
| dc.subject.hal | Physique [physics]/Mécanique [physics]/Mécanique des fluides [physics.class-ph] | |
| dc.subject.hal | Sciences de l'ingénieur [physics]/Mécanique [physics.med-ph]/Mécanique des fluides [physics.class-ph] | |
| dc.subject.hal | Sciences de l'ingénieur [physics]/Milieux fluides et réactifs | |
| bordeaux.journal | Applied Mathematics Letters | |
| bordeaux.page | 245-251 | |
| bordeaux.volume | 25 | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.issue | 3 | |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| bordeaux.peerReviewed | oui | |
| hal.identifier | hal-00626163 | |
| hal.version | 1 | |
| hal.popular | non | |
| hal.audience | Internationale | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-00626163v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Applied%20Mathematics%20Letters&rft.date=2012&rft.volume=25&rft.issue=3&rft.spage=245-251&rft.epage=245-251&rft.eissn=0893-9659&rft.issn=0893-9659&rft.au=ANGOT,%20Philippe&CALTAGIRONE,%20Jean-Paul&FABRIE,%20Pierre&rft.genre=article |
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