Dakota Reference Manual  Version 6.4
Large-Scale Engineering Optimization and Uncertainty Analysis
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interval_type


Specify how to compute gradients and hessians

Specification

Alias: none

Argument(s): none

Default: forward

Description

The interval_type setting is used to select between forward and central differences in the numerical gradient calculations. The dakota, DOT vendor, and OPT++ vendor routines have both forward and central differences available, the CONMIN and NL2SOL vendor routines support forward differences only, and the NPSOL and NLSSOL vendor routines start with forward differences and automatically switch to central differences as the iteration progresses (the user has no control over this). The following forward difference expression

\[ \nabla f ({\bf x}) \cong \frac{f ({\bf x} + h {\bf e}_i) - f ({\bf x})}{h} \]

and the following central difference expression

\[ \nabla f ({\bf x}) \cong \frac{f ({\bf x} + h {\bf e}_i) - f ({\bf x} - h {\bf e}_i)}{2h} \]

are used to estimate the $i^{th}$ component of the gradient vector.