Journal of Convex Analysis 16 (2009), No. 3, 641--666
Copyright Heldermann Verlag 2009
A Proximity Control Algorithm to Minimize Nonsmooth and Nonconvex Semi-Infinite Maximum Eigenvalue Functions
Pierre Apkarian
Université Paul Sabatier, Institut de Mathématiques, 31062 Toulouse, France
Dominikus Noll
Université Paul Sabatier, Institut de Mathématiques, 31062 Toulouse, France
noll@mip.ups-tlse.fr
Olivier Prot
Université Paul Sabatier, Institut de Mathématiques, 31062 Toulouse, France
Proximity control is a well-known mechanism in bundle method for nonsmooth optimization. Here we show that it can be used to optimize a large class of nonconvex and nonsmooth functions with additional structure. This includes for instance nonconvex maximum eigenvalue functions, and also infinite suprema of such functions.
Keywords: Nonsmooth calculus, nonsmooth optimization, Clarke subdifferential, spectral bundle method, maximum eigenvalue function, semi-infinite problem, H-infinity-norm.
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