Abstract

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.

Author information

Contact details are reproduced from the original publication and may be historical.

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

Keywords

  • Nonsmooth calculus
  • nonsmooth optimization
  • Clarke subdifferential
  • spectral bundle method
  • maximum eigenvalue function
  • semi-infinite problem
  • H-infinity-norm

Suggested citation

P. Apkarian, D. Noll, O. Prot. “A Proximity Control Algorithm to Minimize Nonsmooth and Nonconvex Semi-Infinite Maximum Eigenvalue Functions.” Journal of Convex Analysis 16 (2009), No. 3&4, 641–666.

Copyright Heldermann Verlag 2009