Level set methods for finding saddle points of general Morse index

Abstract

For a real valued function, a point is critical if its derivatives are zero, and a critical point is a saddle point if it is not a local extrema. In this paper, we study algorithms to find saddle points of general Morse index. Our approach is motivated by the multidimensional mountain pass theorem, and extends our earlier work on methods (based on studying the level sets) to find saddle points of mountain pass type. We prove the convergence of our algorithms in the nonsmooth case, and the local superlinear convergence of another algorithm in the smooth finite dimensional case.