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