Graduate Student Seminar

Speaker 1: Mona Hajghassem

Title

Near-optimal multigrid preconditioning for distributed optimal control problems constrained by first order ordinary differential equation

Abstract

We present some recent analytic results regarding multigrid preconditioners for a linear-quadratic distributed optimal control problem constrained by a first-order, linear ordinary differential equation (an initial value problem). This work is motivated by an unexpected half-order drop in approximation we encountered in our quest for designing efficient multigrid preconditioners for space-time distributed optimal control problems constrained by linear parabolic equations. Our attempt to understand the source of this suboptimality has led to the study of the simpler case of the ODE-constrained optimal control problem, where a similar drop in approximation order occurs. The work on the ODE-constrained problem required an interesting analysis that we hope to replicate in analyzing the multigrid methods for parabolic-constrained case.

Speaker 2: Serap Tay

Title

Bounded Confidence Multidimensional Opinion Dynamics in Continuous Time

Abstract

In the bounded confidence opinion dynamics model, the opinion of each agent is only affected by other agents whose opinions lie within a confidence bound. In the case of continuous time bounded confidence opinion dynamics model with scalar opinions, trajectories have been proven to reach an equilibrium asymptotically in time. We generalize this result for vector valued opinions by studying the omega-limit set of the trajectories. We present numerical results supporting convergence of the trajectories.