On an Augmented Lagrangian SQP Method for a Class of Optimal Control Problems in Banach Spaces

Authors:
Nadir Arada;Jean-Pierre Raymond;Fredi Tröltzsch
Affiliations:
Fakultät für Mathematik, Technische Universität Chemnitz, D-09107 Chemnitz, Germany;UMR CNRS MIP, Université Paul Sabatier, 31062 Toulouse Cedex 4, France;Institute für Mathematik, Technische Universität Berlin, Str. d. 17 Juni 136, Sekr. MA 4-5, D-10623, Berlin, Germany
Venue:
Computational Optimization and Applications
Year:
2002

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Abstract

An augmented Lagrangian SQP method is discussed for a class of nonlinear optimal control problems in Banach spaces with constraints on the control. The convergence of the method is investigated by its equivalence with the generalized Newton method for the optimality system of the augmented optimal control problem. The method is shown to be quadratically convergent, if the optimality system of the standard non-augmented SQP method is strongly regular in the sense of Robinson. This result is applied to a test problem for the heat equation with Stefan-Boltzmann boundary condition. The numerical tests confirm the theoretical results.