Speaker: Dr. Summer Atkins, University of Alabama in Huntsville
Title: “Regularization techniques for solving singular control problems in mathematical biology”

Abstract: Optimal control theory has been a promising tool in mathematical biology. In some cases, the problem may have the control variable appear linearly in both the state equations and in the objective functional. The optimal control for such a problem can have a singular region, a region of nonzero measure for which the switching function (the partial derivative of the Hamiltonian with respect to the control) is zero. Finding explicit solutions for the singular case can be particularly difficult, but what's even more challenging is that numerical solvers are prone to oscillatory artifacts. In this talk, we consider using total variation regularization to regularize these oscillatory artifacts, and we demonstrate numerical solutions to multiple biologically relevant singular control problems.  

Join us before the talk at 2:00 pm for tea with our speaker.

The KSU Mathematics Colloquium is a seminar series that brings in researchers from other universities to present results on all areas of Mathematics. The talks are targeted at general audiences of students and professors.