A Trust Region Spectral Bundle Method for Nonconvex Eigenvalue Optimization

We present a nonsmooth optimization technique for nonconvex maximum eigenvalue functions and for nonsmooth 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 accumulation 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, output feedback control, H-synthesis AMS subject classifications. 90C26, 90C22, 93B36, 49J52 DOI. 10.1137/060665191

• Type: Journal
• Year: 2008
• Where: SIAMJO
• Authors: Pierre Apkarian, Dominikus Noll, O. Prot
• Keywords: Eigenvalue Functions, Maximum Eigenvalue Functions, Nonsmooth Optimization Technique, SIAMJO 2008