Christoph Helmberg, M. L. Overton, F. Rendl : The Spectral Bundle Method with Second-Order Information

Author(s):

Christoph Helmberg
M. L. Overton
F. Rendl

Title:

Christoph Helmberg, M. L. Overton, F. Rendl : The Spectral Bundle Method with Second-Order Information

Electronic source:

application/pdf

Preprint series:

Technische Universität Chemnitz, Fakultät für Mathematik (Germany). Preprint 10, 2012

Mathematics Subject Classification:

[]

Abstract:

The spectral bundle method was introduced by Helmberg and Rendl [13] to solve a class of eigenvalue optimization problems that is equivalent to the class of semidefinite programs with the constant trace property. We investigate the feasibility and effectiveness of including full or partial second-order information in the spectral bundle method, building on work of Overton and Womersley [20, 23]. We propose several variations that include second-order information in the spectral bundle method and describe efficient implementations. One of these, namely diagonal scaling based on a low-rank approximation of the second-order model for $\lambda_{\max}$, improves the standard spectral bundle method both with respect to accuracy requirements and computation time.

Keywords:

Language:

English

Publication time:

10/2012