ignore_bounds

Do not respect bounds when computing gradients or Hessians

Specification

• Alias: None

• Arguments: None

• Default: bounds respected

Description

When Dakota computes gradients or Hessians by finite differences and the variables in question have bounds, it by default chooses finite-differencing steps that keep the variables within their specified bounds. Older versions of Dakota generally ignored bounds when computing finite differences. To restore the older behavior, one can add keyword <tt>ignore_bounds</tt> to the <tt>response</tt> specification when <tt>method_source dakota</tt> (or just <tt>dakota</tt>) is also specified.

In forward difference or backward difference computations, honoring bounds is straightforward.

To honor bounds when approximating $\partial f/\partial x_i$ , i.e., component $i$ of the gradient of $f$ , by central differences, Dakota chooses two steps $h_1$ and $h_2$ with $h_1\ne h_2$ , such that $x+h_1{e}_i$ and $x+h_2{e}_i$ both satisfy the bounds, and then computes

$$\frac{\partial f}{\partial x_i}ong\frac{h_2^2(f_1-f_0)-h_1^2(f_2-f_0)}{h_1{h}_2(h_2-h_1)},$$

with $f_0=f(x)$ , $f_1=f(x+h_1{e}_i)$ , and $f_2=f(x+h_2{e}_i)$ .