Characteristic curves for set-valued Hamilton-Jacobi equations

TL;DR

This paper extends the method of characteristics to set-valued Hamilton-Jacobi equations derived from multicriteria calculus of variations, providing a new approach for solving these complex equations.

Contribution

It introduces a novel method of characteristics for set-valued Hamilton-Jacobi equations within a set-valued framework, linked to multicriteria optimization.

Findings

Extended the method of characteristics to set-valued equations

Derived results for the Fenchel conjugate in this context

Provided a framework for solving set-valued Hamilton-Jacobi equations

Abstract

The method of characteristics is extended to set-valued Hamilton-Jacobi equations. This problems 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.