Parametric eigenvalue problems

Eigenvalues of parametric symmetric matrices can often be represented by intervals. The bounds of these intervals can be found by solving an optimization problem. Applications arise from finding parameters of a design to make the first eigenfrequency as large as possible, and for the determination of the Lovász number of a graph. In particular, the largest eigenvalue is a quasi-convex function of the parameters. This fact can be used to develop efficient and probably convergent projection methods.