A Trust-Region Algorithm with Adaptive Stochastic Collocation for PDE Optimization under Uncertainty

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dc.citation.firstpageA1847
dc.citation.issueNumber4
dc.citation.journalTitleSIAM Journal on Scientific Computing
dc.citation.lastpageA1879
dc.citation.volumeNumber35
dc.contributor.authorKouri, D.P.
dc.contributor.authorHeinkenschloss, M.
dc.contributor.authorRidzal, D.
dc.contributor.authorvan Bloemen Waanders, B.G.
dc.date.accessioned2016-02-02T19:17:44Z
dc.date.available2016-02-02T19:17:44Z
dc.date.issued2013
dc.description.abstractThe 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.
dc.identifier.citationKouri, 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.
dc.identifier.doihttp://dx.doi.org/10.1137/120892362
dc.identifier.urihttps://hdl.handle.net/1911/88307
dc.language.isoeng
dc.publisherSIAM
dc.rightsArticle 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.
dc.subject.keywordPDE optimization
dc.subject.keyworduncertainty
dc.subject.keywordstochastic collocation
dc.subject.keywordtrust regions
dc.subject.keywordsparse grids
dc.subject.keywordadaptivity
dc.titleA Trust-Region Algorithm with Adaptive Stochastic Collocation for PDE Optimization under Uncertainty
dc.typeJournal article
dc.type.dcmiText
dc.type.publicationpublisher version
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