A stochastic gradient algorithm with momentum terms for optimal control problems governed by a convection-diffusion equation with random diffusivity
DOI10.1016/j.cam.2022.114919zbMath1504.65273OpenAlexW4308498856MaRDI QIDQ2104094
Hamdullah Yücel, Sıtkı Can Toraman
Publication date: 9 December 2022
Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.cam.2022.114919
Probabilistic methods, particle methods, etc. for boundary value problems involving PDEs (65N75) Monte Carlo methods (65C05) Error bounds for boundary value problems involving PDEs (65N15) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Stochastic partial differential equations (aspects of stochastic analysis) (60H15) PDEs with randomness, stochastic partial differential equations (35R60) Computational methods for stochastic equations (aspects of stochastic analysis) (60H35) Existence theories for optimal control problems involving partial differential equations (49J20) PDE constrained optimization (numerical aspects) (49M41)
Related Items
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Optimal control with stochastic PDE constraints and uncertain controls
- Averaged control and observation of parameter-depending wave equations
- Reduced basis approximation of parametrized optimal flow control problems for the Stokes equations
- Quasi-Monte Carlo methods for elliptic PDEs with random coefficients and applications
- Multigrid and sparse-grid schemes for elliptic control problems with random coefficients
- Finite element approximations of stochastic optimal control problems constrained by stochastic elliptic PDEs
- On solving elliptic stochastic partial differential equations
- Momentum and stochastic momentum for stochastic gradient, Newton, proximal point and subspace descent methods
- Stochastic discontinuous Galerkin methods with low-rank solvers for convection diffusion equations
- Stochastic gradient descent for semilinear elliptic equations with uncertainties
- Averaged control
- Block-Diagonal Preconditioning for Optimal Control Problems Constrained by PDEs with Uncertain Inputs
- A Trust-Region Algorithm with Adaptive Stochastic Collocation for PDE Optimization under Uncertainty
- Stochastic Optimal Robin Boundary Control Problems of Advection-Dominated Elliptic Equations
- An Introduction to Computational Stochastic PDEs
- Constrained Optimization with Low-Rank Tensors and Applications to Parametric Problems with PDEs
- On the treatment of distributed uncertainties in PDE-constrained optimization
- Error Estimates of Stochastic Optimal Neumann Boundary Control Problems
- Sparse Adaptive Tensor Galerkin Approximations of Stochastic PDE-Constrained Control Problems
- Multigrid Methods and Sparse-Grid Collocation Techniques for Parabolic Optimal Control Problems with Random Coefficients
- Block-diagonal preconditioning for spectral stochastic finite-element systems
- Robust Stochastic Approximation Approach to Stochastic Programming
- Fast and Exact Simulation of Stationary Gaussian Processes through Circulant Embedding of the Covariance Matrix
- Optimization Methods for Large-Scale Machine Learning
- Galerkin Finite Element Approximations of Stochastic Elliptic Partial Differential Equations
- An Effective Method for Parameter Estimation with PDE Constraints with Multiple Right-Hand Sides
- Stochastic Collocation for Optimal Control Problems with Stochastic PDE Constraints
- Block Preconditioning of Stochastic Galerkin Problems: New Two-sided Guaranteed Spectral Bounds
- Complexity Analysis of stochastic gradient methods for PDE-constrained optimal Control Problems with uncertain parameters
- A Stochastic Gradient Method With Mesh Refinement for PDE-Constrained Optimization Under Uncertainty
- Robust Optimization of PDEs with Random Coefficients Using a Multilevel Monte Carlo Method
- Projected Stochastic Gradients for Convex Constrained Problems in Hilbert Spaces
- Multilevel Monte Carlo Analysis for Optimal Control of Elliptic PDEs with Random Coefficients
- Some methods of speeding up the convergence of iteration methods
- Stochastic Estimation of the Maximum of a Regression Function
- A Stochastic Approximation Method
- A Quasi-Monte Carlo Method for Optimal Control Under Uncertainty
