Approximate Nullspace Iterations for KKT Systems
Authors:
- Kazufumi ItoKIKazufumi Ito
- Karl KunischKKKarl Kunisch
- Volker SchulzVSVolker Schulz
- Ilia GhermanIGIlia Gherman
- 1 January 2010
- journal article
- Published by Society for Industrial & Applied Mathematics (SIAM) in SIAM Journal on Matrix Analysis and Applications
- Vol. 31 (4) , 1835-1847
Abstract
We investigate a linear iteration scheme for solving Karush–Kuhn–Tucker systems arising from optimization problems with linear equality constraints. The iterations are motivated by the simplicity of the proposed combination of iterations for the forward and adjoint systems that need to be solved and for which efficient solvers may already be available. Convergence results are derived, and their practical relevance is investigated by means of a numerical example.Keywords
This publication has 15 references indexed in Scilit:
- Simultaneous pseudo-time stepping for 3D aerodynamic shape optimizationJournal of Numerical Mathematics, 2008
- Approximate Factorization Constraint Preconditioners for Saddle-Point MatricesSIAM Journal on Scientific Computing, 2006
- Preconditioning of One-Shot Pseudo-Timestepping Methods for Shape OptimizationProceedings in Applied Mathematics and Mechanics, 2005
- Aerodynamic shape optimization using simultaneous pseudo-timesteppingJournal of Computational Physics, 2005
- Parallel Lagrange--Newton--Krylov--Schur Methods for PDE-Constrained Optimization. Part I: The Krylov--Schur SolverSIAM Journal on Scientific Computing, 2005
- Simultaneous Pseudo-Timestepping for PDE-Model Based Optimization ProblemsBIT Numerical Mathematics, 2004
- Reduced Functions, Gradients and Hessians from Fixed-Point Iterations for State EquationsNumerical Algorithms, 2002
- Preconditioned all-at-once methods for large, sparse parameter estimation problemsInverse Problems, 2001
- QMR: a quasi-minimal residual method for non-Hermitian linear systemsNumerische Mathematik, 1991
- A class of iterative methods for solving saddle point problemsNumerische Mathematik, 1989