Symmetric Indefinite Preconditioners for Saddle Point Problems with Applications to PDE-Constrained Optimization Problems
From MaRDI portal
Publication:3516126
DOI10.1137/060660977zbMath1154.65029OpenAlexW1966886095MaRDI QIDQ3516126
Joachim Schöberl, Walter Zulehner
Publication date: 1 August 2008
Published in: SIAM Journal on Matrix Analysis and Applications (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1137/060660977
convergenceregularizationsaddle point problemsconjugate gradient methodsoptimal control problemsKKT systemsPDE-constrained optimization problemsindefinite preconditioners
Newton-type methods (49M15) Iterative numerical methods for linear systems (65F10) Numerical computation of matrix norms, conditioning, scaling (65F35) Existence theories for optimal control problems involving partial differential equations (49J20)
Related Items
Preconditioners for reduced saddle point systems arising in elliptic PDE-constrained optimization problems, Robust preconditioners for PDE-constrained optimization with limited observations, Multilevel and weighted reduced basis method for stochastic optimal control problems constrained by Stokes equations, Optimal Dirichlet control of partial differential equations on networks, A symmetric positive definite preconditioner for saddle-point problems, Learning physics-based models from data: perspectives from inverse problems and model reduction, Preconditioning discretizations of systems of partial differential equations, On block preconditioners for saddle point problems with singular or indefinite (1, 1) block, Preconditioning of Active-Set Newton Methods for PDE-constrained Optimal Control Problems, The split Bregman algorithm applied to PDE-constrained optimization problems with total variation regularization, A reverse augmented constraint preconditioner for Lagrange multiplier methods in contact mechanics, Model Reduction for Parametrized Optimal Control Problems in Environmental Marine Sciences and Engineering, A Fast and Stable Preconditioned Iterative Method for Optimal Control Problem of Wave Equations, A note on preconditioners for complex linear systems arising from PDE-constrained optimization problems, Spectral properties of primal-based penalty preconditioners for saddle point problems, Newton--Picard Preconditioners for Time-Periodic Parabolic Optimal Control Problems, Lopsided shift-splitting preconditioner for saddle point problems with three-by-three structure, Combination preconditioning of saddle point systems for positive definiteness, Analysis on inexact block diagonal preconditioners for elliptic PDE-constrained optimization problems, Computational methods for boundary optimal control and identification problems, One-Shot Approaches to Design Optimzation, Reduced order solution of structured linear systems arising in certain PDE-constrained optimization problems, A Multilevel Correction Method for Optimal Controls of Elliptic Equations, POD-Galerkin model order reduction for parametrized time dependent linear quadratic optimal control problems in saddle point formulation, Crank–Nicolson finite difference schemes for parabolic optimal Dirichlet boundary control problems, Robust finite element discretization and solvers for distributed elliptic optimal control problems, Practical RPCG methods for complex symmetric linear systems, Spectral analysis of inexact constraint preconditioning for symmetric saddle point matrices, Optimal Block Preconditioner for an Efficient Numerical Solution of the Elliptic Optimal Control Problems Using Gmres Solver, Integration based profile likelihood calculation for PDE constrained parameter estimation problems, Iterative solution methods for 3D controlled-source electromagnetic forward modelling of geophysical exploration scenarios, Enhancement of flow measurements using fluid-dynamic constraints, Preconditioners for Krylov subspace methods: An overview, Robust Preconditioning and Error Estimates for Optimal Control of the Convection--Diffusion--Reaction Equation with Limited Observation in Isogeometric Analysis, GMRES with multiple preconditioners, Inexact Dual-Primal Isogeometric Tearing and Interconnecting Methods, Boundary concentrated finite elements for optimal boundary control problems of elliptic PDEs, Convergence analysis of multigrid methods with collective point smoothers for optimal control problems, Stability estimates and structural spectral properties of saddle point problems, A note on functional a posteriori estimates for elliptic optimal control problems, Optimal control with stochastic PDE constraints and uncertain controls, An implicit gradient-descent procedure for minimax problems, Superior properties of the PRESB preconditioner for operators on two-by-two block form with square blocks, Robust Solvers for Maxwell's Equations with Dissipative Boundary Conditions, A Data Scalable Augmented Lagrangian KKT Preconditioner for Large-Scale Inverse Problems, Preconditioning for Allen-Cahn variational inequalities with non-local constraints, Preconditioned iterative methods for the convective FitzHugh-Nagumo equations, Preconditioning of complex symmetric linear systems with applications in optical tomography, Numerical optimal control for problems with random forced SPDE constraints, Domain Decomposition Solvers for Frequency-Domain Finite Element Equations, Robust preconditioning techniques for multiharmonic finite element method with application to time-periodic parabolic optimal control problems, Robust Preconditioners for Multiple Saddle Point Problems and Applications to Optimal Control Problems, Simultaneous optical flow and source estimation: space-time discretization and preconditioning, Dimensionally consistent preconditioning for saddle-point problems, Threshold incomplete factorization constraint preconditioners for saddle-point matrices, Fast image inpainting strategy based on the space-fractional modified Cahn-Hilliard equations, Optimization methods for Dirichlet control problems, A note on preconditioner for the Ohta-Kawasaki equation, A Low-Rank Matrix Equation Method for Solving PDE-Constrained Optimization Problems, Efficient Solvers for Saddle Point Problems with Applications to PDE–Constrained Optimization, Some preconditioners for elliptic PDE-constrained optimization problems, Two fast finite difference schemes for elliptic Dirichlet boundary control problems, Adjoint optimization of pressurized membrane structures using automatic differentiation tools, Domain decomposition solvers for nonlinear multiharmonic finite element equations, On Schwarz-type smoothers for saddle point problems with applications to PDE-constrained optimization problems, Finite element discretization of Darcy's equations with pressure dependent porosity, Preconditioners Based on “Parareal” Time-Domain Decomposition for Time-Dependent PDE-Constrained Optimization, A Fixed-Grid Finite Element Algebraic Multigrid Approach for Interface Shape Optimization Governed by 2-Dimensional Magnetostatics, On the restrictively preconditioned conjugate gradient method for solving saddle point problems, Parameter-robust preconditioning for the optimal control of the wave equation, Preconditioners for regularized saddle point matrices, Null-Space Preconditioners for Saddle Point Systems, Preconditioners for state-constrained optimal control problems with Moreau-Yosida penalty function, PDE-Constrained Optimization with Local Control and Boundary Observations: Robust Preconditioners, Efficient block preconditioners for integral constrained elliptic optimal control problems with finite element approximations, A new approximation of the Schur complement in preconditioners for PDE-constrained optimization, Preconditioned Krylov subspace and GMRHSS iteration methods for solving the nonsymmetric saddle point problems, Preconditioners and Tensor Product Solvers for Optimal Control Problems from Chemotaxis, On Fixed-Point, Krylov, and $2\times 2$ Block Preconditioners for Nonsymmetric Problems