Level set methods for finding critical points of mountain pass type

Details Level set methods for finding critical points of mountain pass type Level set methods for finding critical points of mountain pass type

2009-06-24

arxiv.org/abs/0906.4466v2

Nonlinear Anal., 2011, 74:12, 4058--4082

Mathematics

Numerical Analysis

Minor modifications in prose (no change in statements of results or proofs), and reorganization in Section 7 after referee rev

Scientific paper

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.

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