English

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.

Keywords

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

R2 v1 2026-06-21T13:17:20.138Z