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.

PDF file (172kB).