A spectral bundle method with bounds

Semide nite relaxations of quadratic 0-1 programming or graph partitioning problems are well known to be of high quality. However, solving them by primaldual 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 eÆciently large structured equality-constrained semide nite programs if the trace of the primal matrix variable is xed, 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.