Level set methods for finding critical points of mountain pass type
Numerical Analysis
2011-06-14 v2 Analysis of PDEs
Optimization and Control
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.
Cite
@article{arxiv.0906.4466,
title = {Level set methods for finding critical points of mountain pass type},
author = {Adrian S. Lewis and C. H. Jeffrey Pang},
journal= {arXiv preprint arXiv:0906.4466},
year = {2011}
}
Comments
Minor modifications in prose (no change in statements of results or proofs), and reorganization in Section 7 after referee review