Level set methods for finding critical points of mountain pass type
arXiv:0906.4466
Abstract
Computing mountain passes is a standard way of finding critical points. We describe a numerical method for finding critical points that is convergent in the nonsmooth case and locally superlinearly convergent in the smooth finite dimensional case. We apply these techniques to describe a strategy for the Wilkinson problem of calculating the distance of a matrix to a closest matrix with repeated eigenvalues. Finally, we relate critical points of mountain pass type to nonsmooth and metric critical point theory.
Minor modifications in prose (no change in statements of results or proofs), and reorganization in Section 7 after referee review