Please use this identifier to cite or link to this item: http://hdl.handle.net/1822/57890

TitleNormality of necessary optimality conditions for calculus of variations problems with state constraints
Author(s)Khalil, N.
Lopes, S. O.
KeywordsCalculus of variations
Constraint qualification
Normality
Optimal control
Neighboring feasible trajectories
Issue date2019
PublisherSpringer
JournalSet-Valued and Variational Analysis
Abstract(s)We consider non-autonomous calculus of variations problems with a state constraint represented by a given closed set. We prove that if the interior of the Clarke tangent cone of the state constraint set is non-empty (this is the constraint qualification that we suggest here), then the necessary optimality conditions apply in the normal form. We establish normality results for (weak) local minimizers and global minimizers, employing two different approaches and invoking slightly diverse assumptions. More precisely, for the local minimizers result, the Lagrangian is supposed to be Lipschitz with respect to the state variable, and just lower semicontinuous in its third variable. On the other hand, the approach for the global minimizers result (which is simpler) requires the Lagrangian to be convex wit respect to its third variable, but the Lipschitz constant of the Lagrangian with respect to the state variable might now depend on time.
TypeArticle
URIhttp://hdl.handle.net/1822/57890
DOI10.1007/s11228-018-0498-z
ISSN1877-0533
Peer-Reviewedyes
AccessRestricted access (UMinho)
Appears in Collections:PHYSICS OF QUANTUM MATERIALS AND BIONANOSTRUCTURES (2018 - ...)

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