Application of the Augmented Lagrangian-SQP Method to Optimal Control Problems for the Stationary Burgers Equation

Authors:
S. Volkwein
Affiliations:
Institut für Mathematik, Karl-Franzens-Universiät Graz, Heinrichstraße 36, A-8010 Graz, Austria. stefan.volkwein@kfunigraz.ac.at
Venue:
Computational Optimization and Applications
Year:
2000

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Abstract

In this paper optimal control problems for the stationary Burgers equation are analyzed. To solve the optimal control problems the augmented Lagrangian-SQP method is applied. This algorithm has second-order convergence rate depending upon a second-order sufficient optimality condition. Using piecewise linear finite elements it is proved that the discretized augmented Lagrangian-SQP method is well-defined and has second-order rate of convergence. This result is based on the proof of a uniform discrete Babuška-Brezzi condition and a uniform second-order sufficient optimality condition.