1. Michael Overton Scientific Computing Group Broad Interests
Optimization: convex and nonconvex problems from many applications
Numerical linear algebra, especially involving eigenvalues
Floating point arithmetic and the IEEE floating point standard

2. Current Projects
Preconditioning techniques for semidefinite programming (convex optimization in the space of real symmetric matrices)
Matrix distance problems, such as the distance from a given matrix to the nearest matrix with multiple eigenvalues, or the distance from a controllable matrix pair to the nearest uncontrollable matrix pair
Quasi-Newton methods for nonsmooth, nonconvex optimization
Software for H fixed-order controller design via nonsmooth, nonconvex optimization
Optimization of functions of the spectrum (eigenvalues) or pseudospectrum (a more robust alternative) of nonsymmetric matrices
Optimization of functions of the roots of polynomials