A sensitivity-based extrapolation technique for the numerical solution of state-constrained optimal control problems

Michael Hintermüller^1,2 and Irwin Yousept³

¹ Department of Mathematics Humboldt-University of Berlin, Unter den Linden 6, 10099 Berlin, Germany. hint@math.hu-berlin.de
² Institute of Mathematics and Scientific Computing, University of Graz, 8010 Graz, Austria.
³ Institut für Mathematik, Technische Universität Berlin, Str. des 17. Juni 136, 10623 Berlin, Germany. yousept@math.tu-berlin.de

Received: 13 July 2007
Revised: 28 January 2009

Abstract

Sensitivity analysis (with respect to the regularization parameter) of the solution of a class of regularized state constrained optimal control problems is performed. The theoretical results are then used to establish an extrapolation-based numerical scheme for solving the regularized problem for vanishing regularization parameter. In this context, the extrapolation technique provides excellent initializations along the sequence of reducing regularization parameters. Finally, the favorable numerical behavior of the new method is demonstrated and a comparison to classical continuation methods is provided.