Publikation: A method of a-posteriori error estimation with application to proper orthogonal decomposition
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2012
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Zusammenfassung
We consider the following problem of error estimation for the optimal control of nonlinear parabolic partial differential equations: Let an arbitrary admissible control function be given. How far is it from the next locally optimal control? Under natural assumptions including a second-order sufficient optimality condition for the (unknown) locally optimal control, we estimate the distance between the two controls. To do this, we need some information on the lowest eigenvalue of the reduced Hessian. We apply this technique to a model reduced optimal control problem obtained by proper orthogonal decomposition (POD). The distance between a local solution of the reduced problem to a local solution of the original problem is estimated.
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Fachgebiet (DDC)
510 Mathematik
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Optimal control, semilinear partial differential equations, error estimation, proper orthogonal decomposition
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KAMMANN, Eileen, Fredi TRÖLTZSCH, Stefan VOLKWEIN, 2012. A method of a-posteriori error estimation with application to proper orthogonal decompositionBibTex
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<dcterms:abstract xml:lang="eng">We consider the following problem of error estimation for the optimal control of nonlinear parabolic partial differential equations: Let an arbitrary admissible control function be given. How far is it from the next locally optimal control? Under natural assumptions including a second-order sufficient optimality condition for the (unknown) locally optimal control, we estimate the distance between the two controls. To do this, we need some information on the lowest eigenvalue of the reduced Hessian. We apply this technique to a model reduced optimal control problem obtained by proper orthogonal decomposition (POD). The distance between a local solution of the reduced problem to a local solution of the original problem is estimated.</dcterms:abstract>
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