The minimization of a multiobjective Lagrangian with non-constant discount is studied. The problem is embedded into a set-valued framework and a corresponding definition of the value function is given. Bellman's optimality principle and Hopf-Lax formula are derived. The value function is shown to be a solution of a set-valued Hamilton-Jacobi equation.
Visetti, D. (2023). The Hopf-Lax formula for multiobjective costs with non-constant discount via set optimization. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 519(2 (15 March 2023)) [10.1016/j.jmaa.2022.126828].
The Hopf-Lax formula for multiobjective costs with non-constant discount via set optimization
Visetti D.
Primo
2023
Abstract
The minimization of a multiobjective Lagrangian with non-constant discount is studied. The problem is embedded into a set-valued framework and a corresponding definition of the value function is given. Bellman's optimality principle and Hopf-Lax formula are derived. The value function is shown to be a solution of a set-valued Hamilton-Jacobi equation.
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