The simplest test for optimality of each in the basic local minimizer algorithm 2.1 involves the following gradient condition:

The parameter is a small positive number such as
square root of * machine precision*,
( is the smallest number such that the floating
point value of
is greater than the floating representation of 1).
For large-scale problems, the Euclidean
norm divided by , or the * max* norm,
,
may be used to replace or
in the left side of equation (26).
This measures instead an average gradient element.