A Trust-Region Algorithm with Adaptive Stochastic Collocation for PDE Optimization under Uncertainty
| dc.citation.firstpage | A1847 | en_US |
| dc.citation.issueNumber | 4 | en_US |
| dc.citation.journalTitle | SIAM Journal on Scientific Computing | en_US |
| dc.citation.lastpage | A1879 | en_US |
| dc.citation.volumeNumber | 35 | en_US |
| dc.contributor.author | Kouri, D.P. | en_US |
| dc.contributor.author | Heinkenschloss, M. | en_US |
| dc.contributor.author | Ridzal, D. | en_US |
| dc.contributor.author | van Bloemen Waanders, B.G. | en_US |
| dc.date.accessioned | 2016-02-02T19:17:44Z | en_US |
| dc.date.available | 2016-02-02T19:17:44Z | en_US |
| dc.date.issued | 2013 | en_US |
| dc.description.abstract | The numerical solution of optimization problems governed by partial differential equations (PDEs) with random coefficients is computationally challenging because of the large number of deterministic PDE solves required at each optimization iteration. This paper introduces an efficient algorithm for solving such problems based on a combination of adaptive sparse-grid collocation for the discretization of the PDE in the stochastic space and a trust-region framework for optimization and fidelity management of the stochastic discretization. The overall algorithm adapts the collocation points based on the progress of the optimization algorithm and the impact of the random variables on the solution of the optimization problem. It frequently uses few collocation points initially and increases the number of collocation points only as necessary, thereby keeping the number of deterministic PDE solves low while guaranteeing convergence. Currently an error indicator is used to estimate gradient errors due to adaptive stochastic collocation. The algorithm is applied to three examples, and the numerical results demonstrate a significant reduction in the total number of PDE solves required to obtain an optimal solution when compared with a Newton conjugate gradient algorithm applied to a fixed high-fidelity discretization of the optimization problem. | en_US |
| dc.identifier.citation | Kouri, D.P., Heinkenschloss, M., Ridzal, D., et al.. "A Trust-Region Algorithm with Adaptive Stochastic Collocation for PDE Optimization under Uncertainty." <i>SIAM Journal on Scientific Computing,</i> 35, no. 4 (2013) SIAM: A1847-A1879. http://dx.doi.org/10.1137/120892362. | en_US |
| dc.identifier.doi | http://dx.doi.org/10.1137/120892362 | en_US |
| dc.identifier.uri | https://hdl.handle.net/1911/88307 | en_US |
| dc.language.iso | eng | en_US |
| dc.publisher | SIAM | en_US |
| dc.rights | Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. | en_US |
| dc.subject.keyword | PDE optimization | en_US |
| dc.subject.keyword | uncertainty | en_US |
| dc.subject.keyword | stochastic collocation | en_US |
| dc.subject.keyword | trust regions | en_US |
| dc.subject.keyword | sparse grids | en_US |
| dc.subject.keyword | adaptivity | en_US |
| dc.title | A Trust-Region Algorithm with Adaptive Stochastic Collocation for PDE Optimization under Uncertainty | en_US |
| dc.type | Journal article | en_US |
| dc.type.dcmi | Text | en_US |
| dc.type.publication | publisher version | en_US |
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