Set optimization approach for a multi-objective Lagrangian: value function, Hopf-Lax formula and Hamilton-Jacobi equation

Luogo: Povo Zero, via Sommarive 14 (Povo) – Sala Seminari "-1"
Ore: 15:00  

Relatrice:

• Daniela Visetti (Università di Bolzano)    

Abstract:

The complete-lattice approach is introduced, recalling the concepts of difference of sets, set valued functions, Aumann integral and derivatives. A multi-objective calculus of variations problem is considered which is turned into a set-valued problem by a straightforward extension. A new set-valued value function is introduced, for which a Bellman's optimality principle holds. Also the classical result of the Hopf-Lax formula holds for the generalized value function. Finally, the value function is proved to be a solution of a corresponding Hamilton-Jacobi equation.

Referente: Fabio Bagagiolo