An interior point method designed for solving linear quadratic optimal control problems with hp finite elements

We consider linear quadratic optimal control problems with elliptic partial differential equations. The problem is solved with an interior point method in the control variable. We prove convergence of this method in function space by employing a suitable smoothing operator. As discretization we choo...

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Bibliographic Details
Published in:Optimization methods & software 2015-11, Vol.30 (6), p.1276-1302
Main Authors: Wachsmuth, D., Wurst, J.-E.
Format: Article
Language:English
Subjects:
adaptive refinement
Computer programs
control constraints
Discretization
Estimates
Finite element analysis
Function space
hp-finite elements
interior point method
Linear quadratic
Mathematical analysis
Mathematical models
Optimal control
Optimization
Queuing theory
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Summary:We consider linear quadratic optimal control problems with elliptic partial differential equations. The problem is solved with an interior point method in the control variable. We prove convergence of this method in function space by employing a suitable smoothing operator. As discretization we choose hp-finite element method based on local estimates on the smoothness of functions. A fully adaptive algorithm is implemented and a-posteriori error estimators are derived for the central path and the Newton system. The theoretical results are complemented by numerical examples.
ISSN:1055-6788
1029-4937
DOI:10.1080/10556788.2015.1045067