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A Posteriori Estimates for Cost Functionals of Optimal Control Problems

In: Numerical Mathematics and Advanced Applications

Author

Listed:
  • Alexandra Gaevskaya

    (Universität Augsburg, Institute of Mathematics)

  • Ronald H.W. Hoppe

    (Universität Augsburg, Institute of Mathematics
    University of Houston, Department of Mathematics)

  • Sergey Repin

    (Russian Academy of Sciences, St. Petersburg Division of the Steklov Mathematical Institute)

Abstract

A posteriori analysis has become an inherent part of numerical mathematics. Methods of a posteriori error estimation for finite element approximations were actively developed in the last two decades (see, e.g., [1, 2, 3, 12] and the references therein). For problems in the theory of optimization, these methods started receiving attention much later. In particular, for optimal control problems governed by PDEs the literature on this matter is rather scarce. In this work, we present a new approach to a class of optimal control problems associated with elliptic type partial differential equations. In the framework of this approach, we obtain directly computable upper bounds for the cost functionals of the respective optimal control problems.

Suggested Citation

  • Alexandra Gaevskaya & Ronald H.W. Hoppe & Sergey Repin, 2006. "A Posteriori Estimates for Cost Functionals of Optimal Control Problems," Springer Books, in: Alfredo Bermúdez de Castro & Dolores Gómez & Peregrina Quintela & Pilar Salgado (ed.), Numerical Mathematics and Advanced Applications, pages 308-316, Springer.
    • Handle: RePEc:spr:sprchp:978-3-540-34288-5_24
    DOI: 10.1007/978-3-540-34288-5_24
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