Spectral bundle methods for non-convex maximum eigenvalue functions: first-order methods

Authors:
Dominikus Noll;Pierre Apkarian
Affiliations:
Institut de Mathématiques, Université Paul Sabatier, 118, route de Narbonne, 31062, Toulouse, France;Control System Department, CERT-ONERA, 2, avenue Edouard Bélin, 31055, Toulouse, France
Venue:
Mathematical Programming: Series A and B
Year:
2005

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Abstract

Many challenging problems in automatic control may be cast as optimization programs subject to matrix inequality constraints. Here we investigate an approach which converts such problems into non-convex eigenvalue optimization programs and makes them amenable to non-smooth analysis techniques like bundle or cutting plane methods. We prove global convergence of a first-order bundle method for programs with non-convex maximum eigenvalue functions.