KOPS - The Institutional Repository of the University of Konstanz

Multiobjective Optimal Control of a Non-Smooth Semilinear Elliptic Partial Differential Equation

Multiobjective Optimal Control of a Non-Smooth Semilinear Elliptic Partial Differential Equation

Cite This

Files in this item

Files Size Format View

There are no files associated with this item.

CHRISTOF, Constantin, Georg MÜLLER, 2020. Multiobjective Optimal Control of a Non-Smooth Semilinear Elliptic Partial Differential Equation. In: European Series in Applied and Industrial Mathematics (ESAIM) : Control, Optimisation and Calculus of Variations. EDP Sciences. ISSN 1292-8119. eISSN 1262-3377

@article{Christof2020Multi-48751, title={Multiobjective Optimal Control of a Non-Smooth Semilinear Elliptic Partial Differential Equation}, url={https://spp1962.wias-berlin.de/preprints/130.pdf}, year={2020}, issn={1292-8119}, journal={European Series in Applied and Industrial Mathematics (ESAIM) : Control, Optimisation and Calculus of Variations}, author={Christof, Constantin and Müller, Georg} }

<rdf:RDF xmlns:dcterms="http://purl.org/dc/terms/" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:bibo="http://purl.org/ontology/bibo/" xmlns:dspace="http://digital-repositories.org/ontologies/dspace/0.1.0#" xmlns:foaf="http://xmlns.com/foaf/0.1/" xmlns:void="http://rdfs.org/ns/void#" xmlns:xsd="http://www.w3.org/2001/XMLSchema#" > <rdf:Description rdf:about="https://kops.uni-konstanz.de/rdf/resource/123456789/48751"> <dcterms:rights rdf:resource="https://rightsstatements.org/page/InC/1.0/"/> <dc:language>eng</dc:language> <bibo:uri rdf:resource="https://kops.uni-konstanz.de/handle/123456789/48751"/> <dspace:isPartOfCollection rdf:resource="https://kops.uni-konstanz.de/rdf/resource/123456789/39"/> <dc:rights>terms-of-use</dc:rights> <dcterms:available rdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">2020-02-24T12:06:51Z</dcterms:available> <dc:date rdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">2020-02-24T12:06:51Z</dc:date> <dcterms:title>Multiobjective Optimal Control of a Non-Smooth Semilinear Elliptic Partial Differential Equation</dcterms:title> <dc:contributor>Müller, Georg</dc:contributor> <void:sparqlEndpoint rdf:resource="http://localhost/fuseki/dspace/sparql"/> <dcterms:isPartOf rdf:resource="https://kops.uni-konstanz.de/rdf/resource/123456789/39"/> <dc:contributor>Christof, Constantin</dc:contributor> <dc:creator>Christof, Constantin</dc:creator> <dcterms:issued>2020</dcterms:issued> <dcterms:abstract xml:lang="eng">This paper is concerned with the derivation and analysis of first-order necessary optimality conditions for a class of multiobjective optimal control problems governed by an elliptic non-smooth semilinear partial differential equation. Using an adjoint calculus for the inverse of the non-linear and non-differentiable directional derivative of the solution map of the considered PDE, we extend the concept of strong stationarity to the multiobjective setting and demonstrate that the properties of weak and proper Pareto stationarity can also be characterized by suitable multiplier systems that involve both primal and dual quantities. The established optimality conditions imply in particular that Pareto stationary points possess additional regularity properties and that mollification approaches are - in a certain sense - exact for the studied problem class. We further show that the obtained results are closely related to rather peculiar hidden regularization effects that only reveal themselves when the control is eliminated and the problem is reduced to the state. This observation is also new for the case of a single objective function. The paper concludes with numerical experiments that illustrate that the derived optimality systems are amenable to numerical solution procedures.</dcterms:abstract> <foaf:homepage rdf:resource="http://localhost:8080/jspui"/> <dc:creator>Müller, Georg</dc:creator> </rdf:Description> </rdf:RDF>

This item appears in the following Collection(s)

Search KOPS


Browse

My Account