A Spectral Bundle Method with Bounds

C. Helmberg and K.C. Kiwiel

Semidefinite relaxations of quadratic 0-1 programming or graph partitioning problems are well known to be of high quality. However, solving them by primal-dual interior point methods can take much time even for problems of moderate size. The recent spectral bundle method of Helmberg and Rendl can solve quite efficiently large structured equality-constrained semidefinite programs if the trace of the primal matrix variable is fixed, as happens in many applications. We extend the method so that it can handle inequality constraints without seriously increasing computation time. Encouraging preliminary computational results are reported.

Preprint SC 99-37, Konrad-Zuse-Zentrum fuer Informationstechnik Berlin, 14195 Berlin, Germany, December 1999

Contact: helmberg@zib.de