Discretization of interior point methods for state constrained elliptic optimal control problems: optimal error estimates and parameter adjustment

Authors:
Michael Hinze;Anton Schiela
Affiliations:
Schwerpunkt Optimierung und Approximation, Universität Hamburg, Hamburg, Germany 20146;Konrad Zuse Zentrum Berlin, Berlin, Germany 14195
Venue:
Computational Optimization and Applications
Year:
2011

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Abstract

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.