  The problem of computing saddle points is important in certain problems in
numerical partial differential equations and computational chemistry, and is
often solved numerically by a minimization problem over a set of mountain
passes. We point out that a good global mountain pass algorithm should have
good local and global properties. Next, we define the parallel distance, and
show that the square of the parallel distance has a quadratic property. We show
how to design algorithms for the mountain pass problem based on perturbing
parameters of the parallel distance, and that methods based on the parallel
distance have midrange local and global properties.
