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 |
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| container_title | Calculus of variations and partial differential equations |
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| creator | Ennaji, Hamza Igbida, Noureddine Nguyen, Van Thanh |
| description | 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. |
| doi_str_mv | 10.1007/s00526-021-02092-5 |
| format | Article |
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| subjects | Analysis Approximation Calculus of Variations and Optimal Control Optimization Control Finite difference method Mathematical analysis Mathematical and Computational Physics Mathematics Mathematics and Statistics Numerical methods Optimal control Systems Theory Theoretical |
| title | Augmented Lagrangian methods for degenerate Hamilton–Jacobi equations |
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