Reduced order solution of structured linear systems arising in certain PDE-constrained optimization problems
type: Item
instance of: scholarly article
title: Reduced order solution of structured linear systems arising in certain PDE-constrained optimization problems
zbMATH Open document ID: 1266.49061
published in: Computational Optimization and Applications
publication date: 2013-01-04T00:00:00Z
review text: The author investigates solving of structured algebraic linear systems whose blocks stem from the discretized first-order optimality conditions for PDE-constrained optimal control problems. The numerical solution of the corresponding large scale system is analyzed. An ordered reduction is performed firstly and the reduced system is solved iteratively using specifically designed preconditioning techniques. The analysis is completed by numerical experiments on an Dirichlet problem for the Poisson equation and on a simplified Monge-Kantorovich mass transfer problem.
reviewed by: Igor Bock
Mathematics Subject Classification ID: 49M30
Mathematics Subject Classification ID: 49K20
Mathematics Subject Classification ID: 49M25
Mathematics Subject Classification ID: 35J20
Mathematics Subject Classification ID: 49Q20
zbMATH DE Number: 6121893
zbMATH Keywords: structured linear systems
zbMATH Keywords: iterative methods
zbMATH Keywords: PDE-constraints
zbMATH Keywords: optimization
zbMATH Keywords: preconditioning
author: Valeria Simoncini
describes a project that uses: Matlab
describes a project that uses: JDQR
describes a project that uses: JDQZ
describes a project that uses: BNDSCO
describes a project that uses: HSL_MI20
MaRDI profile type: Publication
full work available at URL: s10589-012-9464-0
OpenAlex ID: W2095237535
cites work: Templates for the Solution of Algebraic Eigenvalue Problems
cites work: Preconditioned MHSS iteration methods for a class of block two-by-two linear systems with applications to distributed control problems
cites work: A preconditioning technique for a class of PDE-constrained optimization problems
cites work: Numerical solution of saddle point problems
cites work: Inexact constraint preconditioners for linear systems arising in interior point methods
cites work: Multigrid Methods for PDE Optimization
cites work: HSL_MI20 : An efficient AMG preconditioner for finite element problems in 3D
cites work: Algebraic multigrid theory: The symmetric case
cites work: Augmentation block preconditioners for saddle point-type matrices with singular (1, 1) blocks
cites work: Implicit-Factorization Preconditioning and Iterative Solvers for Regularized Saddle-Point Systems
cites work: Indefinitely preconditioned conjugate gradient method for large sparse equality and inequality constrained quadratic problems
cites work: Q5702543
cites work: Spectral Analysis of Saddle Point Matrices with Indefinite Leading Blocks
cites work: On the solution of equality constrained quadratic programming problems arising in optimization
cites work: Preconditioners for saddle point linear systems with highly singular \((1,1)\) blocks
cites work: An analysis of low-rank modifications of preconditioners for saddle point systems
cites work: Preconditioned all-at-once methods for large, sparse parameter estimation problems
cites work: Preconditioned Conjugate Gradient Method for Optimal Control Problems with Control and State Constraints
cites work: On block preconditioners for saddle point problems with singular or indefinite (1,1) block.
cites work: Q4940821
cites work: Preconditioning discretizations of systems of partial differential equations.
cites work: Acquired Clustering Properties and Solution of Certain Saddle Point Systems
cites work: Block-diagonal and indefinite symmetric preconditioners for mixed finite element formulations
cites work: Q3585634
cites work: Preconditioning Iterative Methods for the Optimal Control of the Stokes Equations
cites work: A Preconditioner for Linear Systems Arising From Interior Point Optimization Methods
cites work: Block-triangular preconditioners for PDE-constrained optimization
cites work: A Flexible Inner-Outer Preconditioned GMRES Algorithm
cites work: Symmetric Indefinite Preconditioners for Saddle Point Problems with Applications to PDE-Constrained Optimization Problems
cites work: Spectral analysis of inexact constraint preconditioning for symmetric saddle point matrices
cites work: A black-box multigrid preconditioner for the biharmonic equation
cites work: Fast Iterative Solution of Stabilised Stokes Systems Part II: Using General Block Preconditioners
cites work: Recent computational developments in Krylov subspace methods for linear systems
cites work: Distributed control and constraint preconditioners
cites work: Q3558349
cites work: Chebyshev semi-iteration in preconditioning for problems including the mass matrix
cites work: Nonstandard Norms and Robust Estimates for Saddle Point Problems
DOI: 10.1007/S10589-012-9464-0
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description: scientific article; zbMATH DE number 6121893