Show simple item record

dc.contributor.advisor Heinkenschloss, Matthias
dc.creatorKouri, Drew
dc.date.accessioned 2012-09-05T23:57:26Z
dc.date.accessioned 2012-09-05T23:57:29Z
dc.date.available 2012-09-05T23:57:26Z
dc.date.available 2012-09-05T23:57:29Z
dc.date.created 2012-05
dc.date.issued 2012-09-05
dc.date.submitted May 2012
dc.identifier.urihttps://hdl.handle.net/1911/64617
dc.description.abstract Using derivative based numerical optimization routines to solve optimization problems governed by partial differential equations (PDEs) with uncertain coefficients is computationally expensive due to the large number of PDE solves required at each iteration. In this thesis, I present an adaptive stochastic collocation framework for the discretization and numerical solution of these PDE constrained optimization problems. This adaptive approach is based on dimension adaptive sparse grid interpolation and employs trust regions to manage the adapted stochastic collocation models. Furthermore, I prove the convergence of sparse grid collocation methods applied to these optimization problems as well as the global convergence of the retrospective trust region algorithm under weakened assumptions on gradient inexactness. In fact, if one can bound the error between actual and modeled gradients using reliable and efficient a posteriori error estimators, then the global convergence of the proposed algorithm follows. Moreover, I describe a high performance implementation of my adaptive collocation and trust region framework using the C++ programming language with the Message Passing interface (MPI). Many PDE solves are required to accurately quantify the uncertainty in such optimization problems, therefore it is essential to appropriately choose inexpensive approximate models and large-scale nonlinear programming techniques throughout the optimization routine. Numerical results for the adaptive solution of these optimization problems are presented.
dc.format.mimetype application/pdf
dc.language.iso eng
dc.subjectApplied mathematics
PDE constrained optimization
Uncertainty Quantification
Trust regions
Adaptivity
Sparse grids
dc.title An Approach for the Adaptive Solution of Optimization Problems Governed by Partial Differential Equations with Uncertain Coefficients
dc.contributor.committeeMember Sorensen, Danny C.
dc.contributor.committeeMember Riviere, Beatrice M.
dc.contributor.committeeMember Cox, Dennis D.
dc.date.updated 2012-09-05T23:57:29Z
dc.identifier.slug 123456789/ETD-2012-05-60
dc.type.genre Thesis
dc.type.material Text
thesis.degree.department Computational and Applied Mathematics
thesis.degree.discipline Engineering
thesis.degree.grantor Rice University
thesis.degree.level Doctoral
thesis.degree.name Doctor of Philosophy
dc.identifier.citation Kouri, Drew. "An Approach for the Adaptive Solution of Optimization Problems Governed by Partial Differential Equations with Uncertain Coefficients." (2012) Diss., Rice University. https://hdl.handle.net/1911/64617.


Files in this item

Thumbnail

This item appears in the following Collection(s)

Show simple item record