A Posteriori Estimates for Cost Functionals of Optimal Control Problems

Alexandra Gaevskaya (), Ronald H.W. Hoppe () and Sergey Repin ()
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Alexandra Gaevskaya: Universität Augsburg, Institute of Mathematics
Ronald H.W. Hoppe: Universität Augsburg, Institute of Mathematics
Sergey Repin: Russian Academy of Sciences, St. Petersburg Division of the Steklov Mathematical Institute

A chapter in Numerical Mathematics and Advanced Applications, 2006, pp 308-316 from Springer

Abstract: 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.

Date: 2006
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DOI: 10.1007/978-3-540-34288-5_24

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