Abstract
The method of characteristics is extended to set-valued Hamilton-Jacobi equations. This problem arises from a calculus of variations’ problem with a multicriteria Lagrangian function: through an embedding into a set-valued framework, a set-valued Hamilton-Jacobi equation is derived, where the Hamiltonian function is the Fenchel conjugate of the Lagrangian function. In this paper a method of characteristics is described and some results are given for the Fenchel conjugate.
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Visetti, D. Characteristic curves for Set-Valued Hamilton-Jacobi Equations. Set-Valued Var. Anal 31, 21 (2023). https://doi.org/10.1007/s11228-023-00685-0
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DOI: https://doi.org/10.1007/s11228-023-00685-0
Keywords
- Multicriteria calculus of variations
- Multiobjective optimization
- Hamilton-jacobi equation
- Characteristics