Global optimization on Stiefel manifolds: a computational approach

The optimization on Stiefel manifolds was discussed by Rapcsák. Here, some methods of global optimization are dealt with and tested on Stiefel manifolds. The structure of the optimizer points of a quadratic problem is studied theoretically and numerically for the lowest interesting dimensional case, as well as the criterion for the finiteness of the number of optimizer points. Then possible reduction tricks are examined together with a numerical study. In the computational investigation we also focused on a special case of the problem, namely when the coefficient matrices in the objective function are diagonal.