Trust region spectral bundle method for nonconvex eigenvalue optimization, submitted

Abstract. We present a non-smooth optimization technique for non-convex maximum eigen-value functions and for non-smooth functions which are infinite maxima of eigenvalue functions. We prove global convergence of our method in the sense that for an arbitrary starting point, every ac-cumulation point of the sequence of iterates is critical. The method is tested on several problems in feedback control synthesis. Key words. Eigenvalue optimization, trust region method, proximity control, spectral bundle, feedback control synthesis, H∞-norm. 1. Introduction. Eigenvalu