Buongiorno
segnalo il seguente seminario
*Martedì 8 Luglio 2025, ore 11:30.*
Aula 3014, Edificio U5, terzo piano, Dipartimento di Matematica e
Applicazioni, via Cozzi 55, Università di Milano-Bicocca
*Speaker*: Lukas Wessels, Georgia Institute of Technology, Atlanta
*Title*: Necessary and Sufficient Conditions for Optimal Control of
Semilinear SPDEs
*Abstract:* In this talk, we consider a finite-horizon optimal control
problem of stochastic reaction-diffusion equations. First we apply the
spike variation method which relies on introducing the first and second
order adjoint state. We give a novel characterization of the second order
adjoint state as the solution to a backward SPDE. Using this
representation, we prove the maximum principle for controlled SPDEs.
As another application of our characterization of the second order adjoint
state, we derive additional necessary optimality conditions in terms of the
value function. These results generalize a classical relationship between
the adjoint states and the derivatives of the value function to the case of
viscosity differentials.
The last part of the talk is devoted to sufficient optimality conditions.
We show how the necessary conditions lead us directly to a non-smooth
version of the classical verification theorem in the framework of viscosity
solutions.
This talk is based on joint works with Wilhelm Stannat.
--
Federica Masiero
Dipartimento di Matematica e Applicazioni,
Università di Milano Bicocca, Edificio U5
via Roberto Cozzi, 55, 20126 Milano