OPTIMIZATION SEMINAR

In this talk we show how the Gauss-Lucas Theorem on the roots of polynimials can be used to study the variational properties of functions of the roots of polynomials. In particular, we show how it can be used to characterize the subdifferentials of the abscissa mapping on polynomials (the maximum of the real parts of the roots) and the radius mapping on polynomilas (the maximum of the modulus of the roots). The abscissa and radius mappings are important for the study of continuous and discrete time linear dynamical systems.

The research described in this talk is joint work with Adrian Lewis of Simon Fraser and Cornell Universities and Michael Overton of the Courant Institute, NYU.

Mathematics Department University of Washington