Level set methods for finding critical points of mountain pass type

In computational chemistry and differential equations, we often seek a critical point of a function by finding a ?mountain pass? between two given points: a connecting path along which the maximum value is minimized. We describe an algorithm that maintains lower bounds on the optimal value by keeping the two points in separate level set components. We prove convergence, even in the nonsmooth case, and local superlinear convergence in the smooth finite dimensional case.