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

Università degli Studi Trento

38123 Povo (TN)

Tel +39 04 61/281508-1625-1701-3786

dept.math [at] unitn.it

**Venue**: Povo Zero, via Sommarive 14 (Povo) – Sala Seminari "-1"**At**: 3:00 p.m.

**Speaker**:

- 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.

**Contact person**: Fabio Bagagiolo