“Some regularity results for minimizers in dynamic optimization”
Lunedì 16 Dicembre 2019, ore 12:15 - Aula seminari 430 - Piernicola Bettiol (Université de Brest, Francia)
We consider the classical problem of the Calculus of Variations introducing a new Weierstrass-type condition for local minimizers of the reference problem. This is a necessary condition which allows to derive important properties of minimizers for a broad class of problems involving a nonautonomous possibly extended-valued Lagrangian.
A first consequence is the Erdmann – Du Bois-Reymond necessary condition expressed in terms of convex subdifferentials and limiting subdifferentials. If the Lagrangian satisfies additional growth conditions (less restrictive than the classical coercivity), this Weierstrass-type condition yields also the Lipschitz regularity of the minimizers.
Similar results can be derived also for higher order problems in the Calculus of Variations.
We shall eventually discuss how these techniques allow to obtain an Erdmann – Du Bois-Reymond necessary condition and minimizers regularity properties for Bolza problems in the context of Optimal Control.
Joint work with C. Mariconda.