inverse eigenvalue problems – Optimization Online

Strong semismoothness of eigenvalues of symmetric matrices and its application to inverse eigenvalue problems

Published: 2001/09/27

Control Applications, Nonsmooth Optimization eigenvalues, inverse eigenvalue problems, newton's methods, quadratic convergence, strong semismoothness, symmetric matrices

It is well known that the eigenvalues of a real symmetric matrix are not everywhere differentiable. A classical result of Ky Fan states that each eigenvalue of a symmetric matrix is the difference of two convex functions. This directly implies that the eigenvalues of a symmetric matrix are semismooth everywhere. Based on a very recent … Read more