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

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