Optimization Governed by Stochastic Partial Differential Equations

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dc.contributor.authorKouri, Drewen_US
dc.date.accessioned2018-06-19T17:46:06Zen_US
dc.date.available2018-06-19T17:46:06Zen_US
dc.date.issued2010-06en_US
dc.date.noteJune 2010en_US
dc.descriptionThis work was also published as a Rice University thesis/dissertation: http://hdl.handle.net/1911/62002en_US
dc.description.abstractThis thesis provides a rigorous framework for the solution of stochastic elliptic partial differential equation (SPDE) constrained optimization problems. In modeling physical processes with differential equations, much of the input data is uncertain (e.g. measurement errors in the diffusivity coefficients). When uncertainty is present, the governing equations become a family of equations indexed by a stochastic variable. Since solutions of these SPDEs enter the objective function, the objective function usually involves statistical moments. These optimization problems governed by SPDEs are posed as a particular class of optimization problems in Banach spaces. This thesis discusses Monte Carlo, stochastic Galerkin, and stochastic collocation methods for the numerical solution of SPDEs and identifies the stochastic collocation method as particularly useful for the optimization of SPDEs. This thesis extends the stochastic collocation method to the optimization context and explores the decoupling nature of this method for gradient and Hessian computations.en_US
dc.format.extent141 ppen_US
dc.identifier.citationKouri, Drew. "Optimization Governed by Stochastic Partial Differential Equations." (2010) <a href="https://hdl.handle.net/1911/102162">https://hdl.handle.net/1911/102162</a>.en_US
dc.identifier.digitalTR10-20en_US
dc.identifier.urihttps://hdl.handle.net/1911/102162en_US
dc.language.isoengen_US
dc.titleOptimization Governed by Stochastic Partial Differential Equationsen_US
dc.typeTechnical reporten_US
dc.type.dcmiTexten_US
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