Preconditioners for Karush-Kuhn-Tucker Matrices
Arising in the Optimal Control of Distributed Systems
Astrid Battermann
Universität Trier
FB IV-Mathematik
Matthias Heinkenschloss
Department of Computational and Applied Mathematics
Rice University
In W. Desch, F. Kappel, and K. Kunisch (eds.)
Optimal Control of Partial Differential Equations
Birkhäuser Verlag, Int. Series of Numer. Math. Vol.126,
Basel, Boston, Berlin, pp.15-32, 1998.
Abstract
In this paper preconditioners for linear systems arising
in interior-point methods for the solution of distributed
control problems are derived and analyzed.
The matrices K
in these systems have a block structure with blocks obtained
from the discretization of the objective function and the governing
differential equation. The preconditioners have a block
structure with blocks being composed of preconditioners for
the subblocks of the system matrix K.
The effectiveness of the preconditioners is
analyzed and numerical examples for
an elliptic model problem are shown.
Keywords
Preconditioners, iterative methods,
interior-point methods, linear quadratic optimal control problems.
1991 Mathematics Subject Classification
49M30, 49N10, 90C06, 90C20.
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