In the RS-PRFO method, the unconstrained space q is split into maximization and minimization subspaces which are defined using the eigenvectors of BL . The goal of RS-PRFO is to find a step that maximizes the energy in the maximization subspace while minimizing the energy in the minimization subspace. To optimize to an order-j saddle point, the j leftmost eigenvectors of BL are assigned to the columns of Ṽ(max) The step in the minimization subspace is found by calculating the leftmost eigenvector of the eigenvalue problem