An efficient alternating direction method of multipliers for optimal control problems constrained by random Helmholtz equations
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Publication:1751062
DOI10.1007/s11075-017-0371-4zbMath1388.93110OpenAlexW2727006385MaRDI QIDQ1751062
Jingshi Li, Kai Zhang, Xiao Shen Wang
Publication date: 23 May 2018
Published in: Numerical Algorithms (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s11075-017-0371-4
Helmholtz equationalternating direction method of multipliersmulti-modes representationrandom optimal control problems
Monte Carlo methods (65C05) Numerical optimization and variational techniques (65K10) Stochastic programming (90C15) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05)
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Cites Work
- Unnamed Item
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- Distributed Optimization and Statistical Learning via the Alternating Direction Method of Multipliers
- Multilevel and weighted reduced basis method for stochastic optimal control problems constrained by Stokes equations
- Optimal control with stochastic PDE constraints and uncertain controls
- On the \(O(1/t)\) convergence rate of the projection and contraction methods for variational inequalities with Lipschitz continuous monotone operators
- Numerical optimal control for problems with random forced SPDE constraints
- Multi-level Monte Carlo finite element method for elliptic PDEs with stochastic coefficients
- Optimal control for two-dimensional stochastic Navier-Stokes equations
- Optimal control of impressed cathodic protection systems in ship building
- An efficient Monte Carlo method for optimal control problems with uncertainty
- Modeling uncertainty in flow simulations via generalized polynomial chaos.
- Nonnegative tensor factorizations using an alternating direction method
- On non-ergodic convergence rate of Douglas-Rachford alternating direction method of multipliers
- 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
- A Trust-Region Algorithm with Adaptive Stochastic Collocation for PDE Optimization under Uncertainty
- Stochastic Optimal Robin Boundary Control Problems of Advection-Dominated Elliptic Equations
- On the $O(1/n)$ Convergence Rate of the Douglas–Rachford Alternating Direction Method
- Sufficient optimality conditions and semi-smooth newton methods for optimal control of stationary variational inequalities
- Numerical PDE-Constrained Optimization
- Weighted Reduced Basis Method for Stochastic Optimal Control Problems with Elliptic PDE Constraint
- Solving Constrained Total-variation Image Restoration and Reconstruction Problems via Alternating Direction Methods
- Alternating Direction Algorithms for $\ell_1$-Problems in Compressive Sensing
- Error Estimates of Stochastic Optimal Neumann Boundary Control Problems
- Deferred Correction Methods for Forward Backward Stochastic Differential Equations
- Optimal control of a stochastic heat equation with boundary-noise and boundary-control
- An Efficient Numerical Method for Acoustic Wave Scattering in Random Media
- Lagrange Multiplier Approach to Variational Problems and Applications
- Optimization with PDE Constraints
- State-Constrained Optimal Control of Semilinear Elliptic Equations with Nonlocal Radiation Interface Conditions
- Optimal control of current in a cathodic protection system: A numerical investigation
- Quasi-Newton Methods and Unconstrained Optimal Control Problems
- Stochastic Collocation for Optimal Control Problems with Stochastic PDE Constraints
- Quasi-Monte Carlo Finite Element Methods for a Class of Elliptic Partial Differential Equations with Random Coefficients
- A Multistep Scheme for Decoupled Forward-Backward Stochastic Differential Equations
- An Adaptive ANOVA-Based Data-Driven Stochastic Method for Elliptic PDEs with Random Coefficient
- Stochastic Collocation on Unstructured Multivariate Meshes
- A Compact Scheme for Coupled Stochastic Nonlinear Schrödinger Equations
- A Stochastic Collocation Method for Elliptic Partial Differential Equations with Random Input Data
