Viscosity solutions of Hamilton-Jacobi-Bellman equations and the infinite horizon problem

Venue: Seminar Room "-1" – Via Sommarive, 14 Povo - Trento
Hour: 15.00 p.m.

• Phu Cuong Le Van - PhD in Mathematics

Abstract:
In this talk, I am devoted to study the Viscosity solutions of Hamilton-JacobiBellman (HJB) equations, in particular its connection to the infinite horizon problem. More precisely, after recalling the notion Viscosity solutions of the general form Hamilton-Jacobi (HJ) equation, I will focus my attention on the optimal control problem, namely infinite horizon problem. From which, the main issues will be driven; at first, I will establish the Dynamical Programming Principle for the problem. Then, we will see how the appropriate Hamilton-Jacobi-Bellman arising by a heuristic argument. Finally, we will prove that the value function associated
to the infinite horizon problem is actually the viscosity solution to the obtained (HJB) and discuss some regularity properties of the value function.

Contact person: 
Fabio Bagagiolo