The best choice is to pick alpha to give the minimum possible energy along the search direction dir. Mathematically, we wish to minimize the function
where 
represents the search direction dir and we write
for alpha. Clearly, this function is a minimum when the
function
has the value zero.
One simple, but effective approach to finding a good estimate of the
zero of 
is to expand this function near 
,
and then to estimate E''(0) by a simple finite difference
where 
is some small ``trial'' value for .
Putting this all together gives the formula
