Normality of Necessary Optimality Conditions for Calculus of Variations Problems with State Constraints

• Type: Article in International Scientific Journal
• Date: 2019

Authors

Khalil, N (Author) FEUP; Lopes, SO (Author) Other

Journal

Title: Set-Valued and Variational Analysis

Vol. 27

Pages: 503-521

ISSN: 1877-0533

Publisher: Springer Nature

Indexing

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Other information

Authenticus ID: P-00P-S05

DOI: 10.1007/s11228-018-0498-z

Abstract (EN): 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 with respect to its third variable, but the Lipschitz constant of the Lagrangian with respect to the state variable might now depend on time.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 19