AUGMENTED LAGRANGIAN METHODS FOR DEGENERATE HAMILTON-JACOBI EQUATIONS

Hamza Ennaji (1) , Noureddine Igbida (1) , Van Thanh Nguyen (2)

1 XLIM - XLIM
2 Department of Mathematics, University of Quynhon, 170 An Duong Vuong, Qui Nhon, Vietnam

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.

Domaines: Equations aux dérivées partielles [math.AP]; Optimisation et contrôle [math.OC]

Hamza Ennaji, Noureddine Igbida, Van Thanh Nguyen. AUGMENTED LAGRANGIAN METHODS FOR DEGENERATE HAMILTON-JACOBI EQUATIONS. 2020. ⟨hal-03020313v1⟩