Discretization of Interior Point Methods for State Constrained Elliptic Optimal Control Problems: Optimal Error Estimates and Parameter Adjustment

Please always quote using this URN: urn:nbn:de:0297-zib-10414
  • An adjustment scheme for the relaxation parameter of interior point approaches to the numerical solution of pointwise state constrained elliptic optimal control problems is introduced. The method is based on error estimates of an associated finite element discretization of the relaxed problems and optimally selects the relaxation parameter in dependence on the mesh size of discretization. The finite element analysis for the relaxed problems is carried out and a numerical example is presented which confirms our analytical findings.

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Metadaten
Author:Michael Hinze, Anton Schiela
Document Type:ZIB-Report
Tag:Elliptic optimal control problem; error estimates; interior point method; pointwise state constraints
MSC-Classification:49-XX CALCULUS OF VARIATIONS AND OPTIMAL CONTROL; OPTIMIZATION [See also 34H05, 34K35, 65Kxx, 90Cxx, 93-XX] / 49Jxx Existence theories / 49J20 Optimal control problems involving partial differential equations
49-XX CALCULUS OF VARIATIONS AND OPTIMAL CONTROL; OPTIMIZATION [See also 34H05, 34K35, 65Kxx, 90Cxx, 93-XX] / 49Kxx Optimality conditions / 49K20 Problems involving partial differential equations
Date of first Publication:2007/11/27
Series (Serial Number):ZIB-Report (07-40)
ISSN:1438-0064
Published in:Also: Priority Program 1253, German Research Foundation (DFG), Preprint-Number SPP1253-08-03 (2007)