A bisection algorithm for the numerical Mountain Pass
  We propose a constructive proof for the Ambrosetti-Rabinowitz Mountain Pass Theorem providing an algorithm, based on a bisection method, for its implementation. The efficiency of our algorithm, particularly suitable for problems in high dimensions, consists in the low number of flow lines to be computed for its convergence; for this reason it improves the one currently used and proposed by Y.S. Choi and P.J. McKenna. 
Vivina Barutello and Susanna Terracini