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Stochastic Collocation for Optimal Control Problems with Stochastic PDE Constraints
9 references·12 citing·31 second hop
Stochastic Collocation for Optimal Control Problems with Stochastic PDE Constraints (2012)Stochastic Collocation for Optimal Contro…High-Order Collocation Methods for Differential Equations with Random Inputs (2005)High-Order Collocation Method…Galerkin Finite Element Approximations of Stochastic Elliptic Partial Differential Equations (2004)Galerkin Finite Element Appro…Modeling uncertainty in flow simulations via generalized polynomial chaos (2003)Modeling uncertainty in flow …The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations (2002)The Wiener--Askey Polynomial …Modeling uncertainty in steady state diffusion problems via generalized polynomial chaos (2002)Modeling uncertainty in stead…A Stochastic Projection Method for Fluid Flow (2002)A Stochastic Projection Metho…Solution of stochastic partial differential equations using Galerkin finite element techniques (2001)Solution of stochastic partia…Stochastic Analysis (1997)Stochastic AnalysisStochastic Finite Elements: A Spectral Approach (1991)Stochastic Finite Elements: A…Taylor Approximation for Chance Constrained Optimization Problems Governed by Partial Differential Equations with High-Dimensional Random Parameters (2021)Taylor Approximation for Chan…A stochastic collocation method based on sparse grids for a stochastic Stokes-Darcy model (2021)A stochastic collocation meth…Taylor approximation and variance reduction for PDE-constrained optimal control under uncertainty (2019)Taylor approximation and vari…Robust Optimization of PDEs with Random Coefficients Using a Multilevel Monte Carlo Method (2019)Robust Optimization of PDEs w…Robust optimisation formulations for the design of an electric machine (2018)Robust optimisation formulati…Optimization of PDEs with Uncertain Inputs (2018)Optimization of PDEs with Unc…Existence and Optimality Conditions for Risk-Averse PDE-Constrained Optimization (2018)Existence and Optimality Cond…An approach for robust PDE-constrained optimization with application to shape optimization of electrical engines and of dynamic elastic structures under uncertainty (2018)An approach for robust PDE-co…Multilevel Monte Carlo Analysis for Optimal Control of Elliptic PDEs with Random Coefficients (2017)Multilevel Monte Carlo Analys…Mean-Variance Risk-Averse Optimal Control of Systems Governed by PDEs with Random Parameter Fields Using Quadratic Approximations (2017)Mean-Variance Risk-Averse Opt…Risk-Averse PDE-Constrained Optimization Using the Conditional Value-At-Risk (2016)Risk-Averse PDE-Constrained O…SENSITIVITY ANALYSIS FOR THE OPTIMIZATION OF RADIOFREQUENCY ABLATION IN THE PRESENCE OF MATERIAL PARAMETER UNCERTAINTY (2012)SENSITIVITY ANALYSIS FOR THE …The stochastic finite-element method (1980)Stochastic Differential Equations: An Introduction with Applications. 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this work references cited by second hop

References

  • 1991Stochastic Finite Elements: A Spectral Approach5,753 cited
  • 2002The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations4,821 cited
  • 2005High-Order Collocation Methods for Differential Equations with Random Inputs1,522 cited
  • 2003Modeling uncertainty in flow simulations via generalized polynomial chaos1,428 cited
  • 1997Stochastic Analysis1,035 cited
  • 2004Galerkin Finite Element Approximations of Stochastic Elliptic Partial Differential Equations869 cited
  • 2002Modeling uncertainty in steady state diffusion problems via generalized polynomial chaos552 cited
  • 2002A Stochastic Projection Method for Fluid Flow503 cited
  • 2001Solution of stochastic partial differential equations using Galerkin finite element techniques414 cited

Cited by

  • 2016Risk-Averse PDE-Constrained Optimization Using the Conditional Value-At-Risk95 cited
  • 2017Mean-Variance Risk-Averse Optimal Control of Systems Governed by PDEs with Random Parameter Fields Using Quadratic Approximations69 cited
  • 2018Existence and Optimality Conditions for Risk-Averse PDE-Constrained Optimization54 cited
  • 2017Multilevel Monte Carlo Analysis for Optimal Control of Elliptic PDEs with Random Coefficients48 cited
  • 2019Taylor approximation and variance reduction for PDE-constrained optimal control under uncertainty

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42 cited
  • 2019Robust Optimization of PDEs with Random Coefficients Using a Multilevel Monte Carlo Method38 cited
  • 2018An approach for robust PDE-constrained optimization with application to shape optimization of electrical engines and of dynamic elastic structures under uncertainty27 cited
  • 2018Optimization of PDEs with Uncertain Inputs25 cited
  • 2021Taylor Approximation for Chance Constrained Optimization Problems Governed by Partial Differential Equations with High-Dimensional Random Parameters21 cited
  • 2012SENSITIVITY ANALYSIS FOR THE OPTIMIZATION OF RADIOFREQUENCY ABLATION IN THE PRESENCE OF MATERIAL PARAMETER UNCERTAINTY16 cited
  • 2021A stochastic collocation method based on sparse grids for a stochastic Stokes-Darcy model13 cited
  • 2018Robust optimisation formulations for the design of an electric machine11 cited