turkmath.org

Optimizing a prescribed eigenvalue of a differential operator or a matrix-valued function depending on parameters has a long history dating back to Euler. The prescribed eigenvalue of interest typically exhibits not only Lipschitz continuity, but also remarkable analyticity properties. We present a numerical approach, based on these analytical properties, for unconstrained optimization of a prescribed eigenvalue of a Hermitian matrix-valued function depending on a few parameters analytically. In the second part, we present a numerical approach for optimization problems with linear objectives and an eigenvalue constraint on the matrix-valued function. The common theme for numerical approaches is the use of global under-estimators for eigenvalue functions, that are built on the variational properties of eigenvalues over the space of Hermitian matrices.