Multigrid Methods for PDE Optimization

From MaRDI portal
Publication:3632438

DOI10.1137/060671590zbMath1167.35354OpenAlexW1992056335MaRDI QIDQ3632438

Volker H. Schulz, Alfio Borzì

Publication date: 11 June 2009

Published in: SIAM Review (Search for Journal in Brave)

Full work available at URL: https://semanticscholar.org/paper/c605456bdda06869d4c15fd81f7fce7bc61df5f3




Related Items

Preconditioners for reduced saddle point systems arising in elliptic PDE-constrained optimization problemsTensor product method for fast solution of optimal control problems with fractional multidimensional Laplacian in constraintsSmoothing Analysis of Two Robust Multigrid Methods for Elliptic Optimal Control ProblemsLearning physics-based models from data: perspectives from inverse problems and model reductionA new semi-smooth Newton multigrid method for control-constrained semi-linear elliptic PDE problemsInversion of convection-diffusion equation with discrete sourcesAn inertia-free filter line-search algorithm for large-scale nonlinear programmingA leapfrog multigrid algorithm for the optimal control of parabolic PDEs with Robin boundary conditionsA multigrid solver for Stokes control problemsSparse Adaptive Tensor Galerkin Approximations of Stochastic PDE-Constrained Control ProblemsMAGMA: Multilevel Accelerated Gradient Mirror Descent Algorithm for Large-Scale Convex Composite MinimizationMGOPT with gradient projection method for solving bilinear elliptic optimal control problemsA fast second-order parareal solver for fractional optimal control problemsMultigrid preconditioning of linear systems for semi-smooth Newton methods applied to optimization problems constrained by smoothing operatorsMultigrid and sparse-grid schemes for elliptic control problems with random coefficientsOn a multigrid solver for stationary Navier-Stokes velocity-pressure tracking-type control problemsAdaptive multilevel correction method for finite element approximations of elliptic optimal control problemsOne-Shot Approaches to Design OptimzationReduced order solution of structured linear systems arising in certain PDE-constrained optimization problemsFast interior point solution of quadratic programming problems arising from PDE-constrained optimizationA Multilevel Correction Method for Optimal Controls of Elliptic EquationsRadial basis function networks simulation of age-structure populationBDF2 schemes for optimal parameter control problems governed by bilinear parabolic equationsRobust finite element discretization and solvers for distributed elliptic optimal control problemsMGIC: Multigrid-in-Channels Neural Network ArchitecturesA Semi-Lagrangian Two-Level Preconditioned Newton--Krylov Solver for Constrained Diffeomorphic Image RegistrationOptimal Block Preconditioner for an Efficient Numerical Solution of the Elliptic Optimal Control Problems Using Gmres SolverLarge-Scale Loan Portfolio SelectionNested multigrid methods for time-periodic, parabolic optimal control problemsA new solution for optimal control of fractional convection-reaction-diffusion equation using rational barycentric interpolationA Parallel-In-Time Block-Circulant Preconditioner for Optimal Control of Wave EquationsA Multigrid Approach to SDP Relaxations of Sparse Polynomial Optimization ProblemsLow-Rank Solution to an Optimization Problem Constrained by the Navier--Stokes EquationsMultigrid methods for an elliptic optimal control problem with pointwise state constraintsMultigrid second-order accurate solution of parabolic control-constrained problemsNumerical Multilevel Upscaling for Incompressible Flow in Reservoir Simulation: An Element-Based Algebraic Multigrid (AMGe) ApproachA POD framework to determine robust controls in PDE optimizationConvergence analysis of multigrid methods with collective point smoothers for optimal control problemsOptimal control with stochastic PDE constraints and uncertain controlsA Multilevel Proximal Gradient Algorithm for a Class of Composite Optimization ProblemsA Data Scalable Augmented Lagrangian KKT Preconditioner for Large-Scale Inverse ProblemsMultigrid optimization for DNS-based optimal control in turbulent channel flowsRobust preconditioning techniques for multiharmonic finite element method with application to time-periodic parabolic optimal control problemsA Priori Error Estimates for Finite Element Methods forH(2,1)-Elliptic EquationsConvergence of a two-level ideal algorithm for a parametric shape inverse model problemSome preconditioners for elliptic PDE-constrained optimization problemsA new subspace correction method for nonlinear unconstrained convex optimization problemsTwo fast finite difference schemes for elliptic Dirichlet boundary control problemsA new multigrid method for unconstrained parabolic optimal control problemsOn the treatment of distributed uncertainties in PDE-constrained optimizationA leapfrog semi-smooth Newton-multigrid method for semilinear parabolic optimal control problemsPreconditioners Based on “Parareal” Time-Domain Decomposition for Time-Dependent PDE-Constrained OptimizationFormulation and multigrid solution of Cauchy-Riemann optimal control problemsMultigrid methods for saddle point problems: optimality systemsImplementation and analysis of multigrid schemes with finite elements for elliptic optimal control problemsOn an extension of one-shot methods to incorporate additional constraintsPreconditioned iterative method for boundary value method discretizations of a parabolic optimal control problemOptimal-Order Preconditioners for Linear Systems Arising in the Semismooth Newton Solution of a Class of Control-Constrained ProblemsA Multilevel Approach for Computing the Limited-Memory Hessian and its Inverse in Variational Data AssimilationRobust Optimization of PDEs with Random Coefficients Using a Multilevel Monte Carlo MethodA full multigrid solution of control-constrained Cauchy–Riemann optimal control problemsNon-commutative discretize-then-optimize algorithms for elliptic PDE-constrained optimal control problemsEfficient block preconditioners for integral constrained elliptic optimal control problems with finite element approximationsOn Discrete Shape Gradients of Boundary Type for PDE-constrained Shape OptimizationMG/OPT and Multilevel Monte Carlo for Robust Optimization of PDEsA novel multigrid method for elliptic distributed control problemsA robust all-at-once multigrid method for the Stokes control problem




This page was built for publication: Multigrid Methods for PDE Optimization