Dakota Reference Manual
Version 6.12
Explore and Predict with Confidence

Step size used when computing gradients and Hessians
Alias: fd_gradient_step_size
Argument(s): REALLIST
Default: 0.001
fd_step_size
specifies the relative finite difference step size to be used in the computations. Either a single value may be entered for use with all parameters, or a list of step sizes may be entered, one for each parameter.
The latter option of a list of step sizes is only valid for use with the Dakota finite differencing routine. For Dakota with an interval scaling type of absolute
, the differencing interval will be fd_step_size
.
For Dakota with and interval scaling type of bounds
, the differencing intervals are computed by multiplying fd_step_size
with the range of the parameter. For Dakota (with an interval scaling type of relative
), DOT, CONMIN, and OPT++, the differencing intervals are computed by multiplying the fd_step_size
with the current parameter value. In this case, a minimum absolute differencing interval is needed when the current parameter value is close to zero. This prevents finite difference intervals for the parameter which are too small to distinguish differences in the response quantities being computed. Dakota, DOT, CONMIN, and OPT++ all use .01*fd_step_size
as their minimum absolute differencing interval. With a fd_step_size = .001
, for example, Dakota, DOT, CONMIN, and OPT++ will use intervals of .001*current value with a minimum interval of 1.e5. NPSOL and NLSSOL use a different formula for their finite difference intervals: fd_step_size*(1+current parameter value)
. This definition has the advantage of eliminating the need for a minimum absolute differencing interval since the interval no longer goes to zero as the current parameter value goes to zero.
ROL's finite difference step size can not be controlled via Dakota. Therefore, fd_step_size
will be ignored when ROL's finite differencing routines are used (vendor FD gradients are specified). ROL's differencing intervals are computed by multiplying the current parameter value with the square root of machine precision.