Efficient numerical methods for elliptic optimal control problems with random coefficient
DOI10.3934/era.2020053OpenAlexW3036561748MaRDI QIDQ779918
Jiachuan Zhang, Haiming Song, Xiaowei Pang, Xiao Shen Wang
Publication date: 14 July 2020
Published in: Electronic Research Archive (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.3934/era.2020053
finite element methodoptimal control problemalternating direction method of multiplierMonte Carlo approximationmulti-modes expansion
Monte Carlo methods (65C05) Numerical optimization and variational techniques (65K10) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30)
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Finite element approximations of stochastic optimal control problems constrained by stochastic elliptic PDEs
- Multi-level Monte Carlo finite element method for elliptic PDEs with stochastic coefficients
- On the Schrödinger equation and the eigenvalue problem
- Lower bounds for higher eigenvalues by finite difference methods
- Solving elliptic boundary value problems with uncertain coefficients by the finite element method: the stochastic formulation
- An efficient Monte Carlo method for optimal control problems with uncertainty
- Elliptic partial differential equations of second order
- An efficient alternating direction method of multipliers for optimal control problems constrained by random Helmholtz equations
- Taylor approximation and variance reduction for PDE-constrained optimal control under uncertainty
- An alternating direction method of multipliers for elliptic equation constrained optimization problem
- \(O(1/t)\) complexity analysis of the generalized alternating direction method of multipliers
- Stochastic Galerkin method for elliptic SPDEs: a white noise approach
- Analytic Regularity and GPC Approximation for Control Problems Constrained by Linear Parametric Elliptic and Parabolic PDEs
- A Trust-Region Algorithm with Adaptive Stochastic Collocation for PDE Optimization under Uncertainty
- Numerical PDE-Constrained Optimization
- Error Estimates of Stochastic Optimal Neumann Boundary Control Problems
- An Efficient Numerical Method for Acoustic Wave Scattering in Random Media
- Optimization with PDE Constraints
- A MULTIMODES MONTE CARLO FINITE ELEMENT METHOD FOR ELLIPTIC PARTIAL DIFFERENTIAL EQUATIONS WITH RANDOM COEFFICIENTS
- An Alternating Direction Method of Multipliers for the Optimization Problem Constrained with a Stationary Maxwell System
- A Stochastic Collocation Method for Elliptic Partial Differential Equations with Random Input Data
- A Stochastic Collocation Method for Elliptic Partial Differential Equations with Random Input Data
This page was built for publication: Efficient numerical methods for elliptic optimal control problems with random coefficient