Multigrid Preconditioning of Linear Systems for Interior Point Methods Applied to a Class of Box-constrained Optimal Control Problems

DOI10.1137/100786502zbMath1247.65081arXiv1004.0382OpenAlexW2963896597MaRDI QIDQ2882345

Publication date: 4 May 2012

Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1004.0382

zbMATH Keywords

numerical examples interior point methods PDE-constrained optimization large-scale problems multigrid preconditioning

Mathematics Subject Classification ID

Large-scale problems in mathematical programming (90C06) Numerical optimization and variational techniques (65K10) Numerical methods based on nonlinear programming (49M37) Interior-point methods (90C51) Existence theories for optimal control problems involving partial differential equations (49J20) Preconditioners for iterative methods (65F08)

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Optimal order multigrid preconditioners for the distributed control of parabolic equations with coarsening in space and time ⋮ Multigrid preconditioning of linear systems for semi-smooth Newton methods applied to optimization problems constrained by smoothing operators ⋮ Semi-convergence analysis of the GSS iteration methods for singular saddle point problems ⋮ Fast interior point solution of quadratic programming problems arising from PDE-constrained optimization ⋮ On Block Triangular Preconditioners for the Interior Point Solution of PDE-Constrained Optimization Problems ⋮ Optimal-Order Preconditioners for Linear Systems Arising in the Semismooth Newton Solution of a Class of Control-Constrained Problems ⋮ Multigrid Preconditioners for the Newton--Krylov Method in the Optimal Control of the Stationary Navier--Stokes Equations

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