zahr2019adaptive.bib

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@article{zahr2019adaptive,
  abstract = {This work introduces a new method to efficiently solve optimization problems constrained by partial differential equations (PDEs) with uncertain coefficients. The method leverages two sources of inexactness that trade accuracy for speed: (1) stochastic collocation based on dimension-adaptive sparse grids (SGs), which approximates the stochastic objective function with a limited number of quadrature nodes, and (2) projection-based reduced-order models (ROMs), which generate efficient approximations to PDE solutions. These two sources of inexactness lead to inexact objective function and gradient evaluations, which are managed by a trust-region method that guarantees global convergence by adaptively refining the sparse grid and reduced-order model until a proposed error indicator drops below a tolerance specified by trust-region convergence theory. A key feature of the proposed method is that the error indicator---which accounts for errors incurred by both the sparse grid and reduced-order model---must be only an asymptotic error bound, i.e., a bound that holds up to an arbitrary constant that need not be computed. This enables the method to be applicable to a wide range of problems, including those where sharp, computable error bounds are not available; this distinguishes the proposed method from previous works. Numerical experiments performed on a model problem from optimal flow control under uncertainty verify global convergence of the method and demonstrate the method's ability to outperform previously proposed alternatives.},
  arxiv = {https://arxiv.org/abs/1811.00177},
  author = {Zahr, Matthew J. and Carlberg, Kevin and Kouri, Drew P.},
  contribution = {conceptualization, methodology (MJZ, DPK); software, formal analysis, investigation, writing - original (MJZ); writing - edit/review (KC, DPK)},
  corauthor = {Zahr, Matthew J.},
  date-added = {2015-08-20 14:00:41 +0000},
  date-modified = {2021-03-26 17:31:39 -0400},
  doi = {10.1137/18M1220996},
  journal = {SIAM/ASA Journal on Uncertainty Quantification},
  number = {3},
  pages = {877--912},
  project = {trammo:stochromopt},
  title = {An efficient, globally convergent method for optimization under uncertainty using adaptive model reduction and sparse grids},
  url = {https://epubs.siam.org/doi/10.1137/18M1220996},
  volume = {7},
  year = {2019},
  bdsk-url-1 = {https://epubs.siam.org/doi/10.1137/18M1220996},
  bdsk-url-2 = {https://doi.org/10.1137/18M1220996}
}

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