Preprint 36-2004

The convergence of an interior point method for an elliptic control problem with mixed control-state constraints.

Author(s) : Uwe Prüfert , Fredi Tröltzsch , Martin Weiser

Preprint series of the Institute of Mathematics, Technische Universität Berlin
Preprint 36-2004

MSC 2000

90C51 Interior-point methods

49J20 Optimal control problems involving partial differential equations

ZDM :

CR :

Abstract :
The paper addresses primal interior point method for state constrained PDE optimal control problems. By a Lavrentiev regularization, the state constraint is transformed to a mixed control-state constraint with bounded Lagrange multiplier. Existence and convergence of the central path are established, and linear convergence of a short-step pathfollowing method is shown. The behaviour of the regularizations are demonstrated by numerical examples.

Keywords : interior point methods in function space, optimal control, mixed control-state constraints, Lavrentiev regularization