The spectral bundle method was introduced by Helmberg and Rendl 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. 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 the maximum eigenvalue, improves the standard spectral bundle method both with respect to accuracy requirements and computation time.
Preprint 2012-10, Fakultät für Mathematik, Technische Universität Chemnitz, September 2012.