A Data Scalable Augmented Lagrangian KKT Preconditioner for Large-Scale Inverse Problems
From MaRDI portal
Publication:5372667
DOI10.1137/16M1084365zbMath1422.65090arXiv1607.03556OpenAlexW2963441829MaRDI QIDQ5372667
Nick Alger, Umberto Villa, Omar Ghattas, Tan Bui-Thanh
Publication date: 27 October 2017
Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1607.03556
preconditioningKrylov subspace methodsaugmented Lagrangiandata scalabilityPDE constrained inverse problemsKKT matrix
Numerical optimization and variational techniques (65K10) Iterative numerical methods for linear systems (65F10) Discrete approximations in optimal control (49M25) Preconditioners for iterative methods (65F08)
Related Items
Learning physics-based models from data: perspectives from inverse problems and model reduction ⋮ Simultaneous Identification and Denoising of Dynamical Systems ⋮ Hierarchical Matrix Approximations of Hessians Arising in Inverse Problems Governed by PDEs ⋮ Scalable Matrix-Free Adaptive Product-Convolution Approximation for Locally Translation-Invariant Operators
Uses Software
Cites Work
- Unnamed Item
- Unnamed Item
- Matrix probing: a randomized preconditioner for the wave-equation Hessian
- Convergence analysis of multigrid methods with collective point smoothers for optimal control problems
- A preconditioning technique for a class of PDE-constrained optimization problems
- Automated solution of differential equations by the finite element method. The FEniCS book
- An inverse problem formulation for parameter estimation of a reaction-diffusion model of low grade gliomas
- Analytic Hessian derivation for the quasi-one-dimensional Euler equations
- Some observations on Babuška and Brezzi theories
- Multigrid methods for parabolic distributed optimal control problems
- A multigrid method for distributed parameter estimation problems
- A class of iterative methods for solving saddle point problems
- The convergence rate of the minimal residual method for the Stokes problem
- Algebraic multigrid by smoothed aggregation for second and fourth order elliptic problems
- Stability estimates and structural spectral properties of saddle point problems
- Preconditioning for sparse linear systems at the dawn of the 21st century: history, current developments, and future perspectives
- Analysis of the Hessian for aerodynamic optimization: Inviscid flow
- Robust preconditioners for PDE-constrained optimization with limited observations
- Multigrid solution of a distributed optimal control problem constrained by the Stokes equations
- Analysis of the Hessian for inverse scattering problems. III: Inverse medium scattering of electromagnetic waves in three dimensions.
- Sparsity- and continuity-promoting seismic image recovery with curvelet frames
- Über ein Variationsprinzip zur Lösung von Dirichlet-Problemen bei Verwendung von Teilräumen, die keinen Randbedingungen unterworfen sind. (On a variational principle for solving Dirichlet problems less boundary conditions using subspaces)
- Preconditioned all-at-once methods for large, sparse parameter estimation problems
- A new approximation of the Schur complement in preconditioners for PDE-constrained optimization
- Finite Elements and Fast Iterative Solvers
- Analysis of the Hessian for inverse scattering problems: I. Inverse shape scattering of acoustic waves
- Analysis of the Hessian for inverse scattering problems: II. Inverse medium scattering of acoustic waves
- Preconditioning discretizations of systems of partial differential equations
- Some Convergence Properties of the Conjugate Gradient Method in Hilbert Space
- Fast Algorithms for Source Identification Problems with Elliptic PDE Constraints
- Optimal order multilevel preconditioners for regularized ill-posed problems
- Optimal Solvers for PDE-Constrained Optimization
- Preconditioned Conjugate Gradient Method for Optimal Control Problems with Control and State Constraints
- Efficient Preconditioners for Optimality Systems Arising in Connection with Inverse Problems
- Nonstandard Norms and Robust Estimates for Saddle Point Problems
- Fast Algorithms for Bayesian Uncertainty Quantification in Large-Scale Linear Inverse Problems Based on Low-Rank Partial Hessian Approximations
- A General Interpolation Strategy for Algebraic Multigrid Using Energy Minimization
- Preconditioning Iterative Methods for the Optimal Control of the Stokes Equations
- Hierarchical Interpolative Factorization for Elliptic Operators: Differential Equations
- Numerical solution of saddle point problems
- Symmetric Indefinite Preconditioners for Saddle Point Problems with Applications to PDE-Constrained Optimization Problems
- Mesh Independent Superlinear PCG Rates Via Compact-Equivalent Operators
- Combination Preconditioning and the Bramble–Pasciak$^{+}$ Preconditioner
- Multigrid Methods for PDE Optimization
- A Preconditioning Technique for Indefinite Systems Resulting from Mixed Approximations of Elliptic Problems
- Mixed and Hybrid Finite Element Methods
- Solution of Sparse Indefinite Systems of Linear Equations
- A Note on Preconditioning for Indefinite Linear Systems
- Experiences with a space–time multigrid method for the optimal control of a chemical turbulence model
- Computational Methods for Inverse Problems
- Perspectives in Flow Control and Optimization
- Regularization-Robust Preconditioners for Time-Dependent PDE-Constrained Optimization Problems
- Operator Preconditioning for a Class of Inequality Constrained Optimal Control Problems
- Preconditioners for state-constrained optimal control problems with Moreau-Yosida penalty function
- Multigrid Algorithms for Inverse Problems with Linear Parabolic PDE Constraints
- Superlinear Convergence of Krylov Subspace Methods for Self-Adjoint Problems in Hilbert Space
- Analysis of the Minimal Residual Method Applied to Ill Posed Optimality Systems
- A Fast Solver for anH1Regularized PDE-Constrained Optimization Problem
- Parallel Lagrange--Newton--Krylov--Schur Methods for PDE-Constrained Optimization. Part I: The Krylov--Schur Solver
- Parallel Lagrange--Newton--Krylov--Schur Methods for PDE-Constrained Optimization. Part II: The Lagrange--Newton Solver and Its Application to Optimal Control of Steady Viscous Flows
- An Algebraic Analysis of a Block Diagonal Preconditioner for Saddle Point Systems
