  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.
