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| rdf:type
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| Description
| - Optimalizace a inverzní úlohy pro parciální diferenciální rovnice jsou často formulovány jako úlohy nelineárního programování s omezeními pomocí Lagrangeova formalismu. Nelinearity se řeší sekvenčním kvadratickým programováním. Numerické řešení výsledných sedlo-bodových soustav se pak opírá o iterační metodu. V tomto článku aplikujeme metodu semi-monotónních rozšířených Lagrangiánů, která byla nedávno navržena a analyzována druhým z autorů, a to pro kvadratické programování s rovnostními a jednoduchými omezeními. Tyto úlohy vyvstávají při řešení úloh optimálního řízení a identifikace parametrů. Pomocí předpodmínění multigridem primárního i duálního skalárního součinu a Hessiánu lze ukázat, že algoritmus konverguje v O(1) násobeních matice krát vektor. Numerické výsledky ukazujeme pro segmentaci obrazu a 2-dimenzionální magnetostatiku. (cs)
- Optimization and inverse problems governed by partial differential equations are often formulated as constrained nonlinear programming problems via the Lagrange formalism. The nonlinearity is treated using the sequential quadratic programming. A numerical solution then hinges on an efficient iterative method for the resulting saddle--point systems. In this paper we apply a semi--monotonic augmented Lagrangians method, recently proposed and analyzed by the second author, for equality and simple--bound constrained quadratic programming subproblems arising from optimal control and parameter identification. Provided multigrid preconditioning of primal and dual space inner products and of the Hessian the algorithm converges at $O(1)$ matrix--vector multiplications. Numerical results are given for applications in image segmentation and 2--dimensional magnetostatics discretized using lowest--order Lagrange finite elements.
- Optimization and inverse problems governed by partial differential equations are often formulated as constrained nonlinear programming problems via the Lagrange formalism. The nonlinearity is treated using the sequential quadratic programming. A numerical solution then hinges on an efficient iterative method for the resulting saddle--point systems. In this paper we apply a semi--monotonic augmented Lagrangians method, recently proposed and analyzed by the second author, for equality and simple--bound constrained quadratic programming subproblems arising from optimal control and parameter identification. Provided multigrid preconditioning of primal and dual space inner products and of the Hessian the algorithm converges at $O(1)$ matrix--vector multiplications. Numerical results are given for applications in image segmentation and 2--dimensional magnetostatics discretized using lowest--order Lagrange finite elements. (en)
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| Title
| - Semi-monotonic augmented Lagrangians for optimal control and parameter identification
- Semi-monotonic augmented Lagrangians for optimal control and parameter identification (en)
- Semi-monotonic augmented Lagrangians for optimal control and parameter identification (cs)
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| skos:prefLabel
| - Semi-monotonic augmented Lagrangians for optimal control and parameter identification
- Semi-monotonic augmented Lagrangians for optimal control and parameter identification (en)
- Semi-monotonic augmented Lagrangians for optimal control and parameter identification (cs)
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| skos:notation
| - RIV/61989100:27240/08:00019177!RIV09-MSM-27240___
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| http://linked.open...avai/riv/aktivita
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| http://linked.open...avai/riv/aktivity
| - P(1ET400300415), P(GP201/05/P008), Z(MSM6198910027)
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| http://linked.open...vai/riv/dodaniDat
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| http://linked.open...aciTvurceVysledku
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| http://linked.open.../riv/druhVysledku
| |
| http://linked.open...iv/duvernostUdaju
| |
| http://linked.open...titaPredkladatele
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| http://linked.open...dnocenehoVysledku
| |
| http://linked.open...ai/riv/idVysledku
| - RIV/61989100:27240/08:00019177
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| http://linked.open...riv/jazykVysledku
| |
| http://linked.open.../riv/klicovaSlova
| - constrained quadratic programming; augmented Lagrangians; multigrid; optimal control; parameter identification (en)
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| http://linked.open.../riv/klicoveSlovo
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| http://linked.open...ontrolniKodProRIV
| |
| http://linked.open...v/mistoKonaniAkce
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| http://linked.open...i/riv/mistoVydani
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| http://linked.open...i/riv/nazevZdroje
| - Numerical Mathematics and Advanced Applications - ENUMATH 2007
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| http://linked.open...in/vavai/riv/obor
| |
| http://linked.open...ichTvurcuVysledku
| |
| http://linked.open...cetTvurcuVysledku
| |
| http://linked.open...vavai/riv/projekt
| |
| http://linked.open...UplatneniVysledku
| |
| http://linked.open...iv/tvurceVysledku
| - Dostál, Zdeněk
- Lukáš, Dalibor
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| http://linked.open...vavai/riv/typAkce
| |
| http://linked.open.../riv/zahajeniAkce
| |
| http://linked.open...n/vavai/riv/zamer
| |
| number of pages
| |
| http://purl.org/ne...btex#hasPublisher
| |
| https://schema.org/isbn
| |
| http://localhost/t...ganizacniJednotka
| |
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