Augmented Lagrangian methods for degenerate Hamilton–Jacobi equations

We suggest a new approach to solve a class of degenerate Hamilton–Jacobi equations without any assumptions on the emptiness of the Aubry set. It is based on the characterization of the maximal subsolution by means of the Fenchel–Rockafellar duality. This approach enables us to use augmented Lagrangi...

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Veröffentlicht in:Calculus of variations and partial differential equations 2021-12, Vol.60 (6), Article 238
Hauptverfasser: Ennaji, Hamza, Igbida, Noureddine, Nguyen, Van Thanh
Format: Artikel
Sprache:eng
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Zusammenfassung:We suggest a new approach to solve a class of degenerate Hamilton–Jacobi equations without any assumptions on the emptiness of the Aubry set. It is based on the characterization of the maximal subsolution by means of the Fenchel–Rockafellar duality. This approach enables us to use augmented Lagrangian methods as alternatives to the commonly used methods for numerical approximation of the solution, based on finite difference approximation or on optimal control interpretation of the solution.
ISSN:0944-2669
1432-0835
DOI:10.1007/s00526-021-02092-5