Partial derivatives are used to create the linear approximation to the nonlinear
problem. The default method of calculating derivatives is by perturbing the
value of each variable in turn and calculating derivatives from the changes in the values of
the coefficients.
The alternative is to use analytic derivatives, in which formulae are derived for the derivatives
of each non-constant coefficient. These formulae are then evaluated directly to obtain the
derivatives.
Analytic derivatives cannot be used for formulae involving discontinuous functions (such
as the logical functions
EQ,
LT, etc). They may not work
well with functions which are not smooth (such as
MAX), or where the
derivative changes very quickly with the value of the variable (such as
LOG
of small values).