Dakota Reference Manual: numerical_hessians

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numerical_hessians

Hessians are needed and will be approximated by finite differences

## Specification

Alias: none

Argument(s): none

Child Keywords:

| Required/Optional | Description of Group | Dakota Keyword | Dakota Keyword Description
--- | --- | --- | --- | ---
| Optional | fd_step_size | Step size used when computing gradients and Hessians
| Optional (Choose One) | Step Scaling (Group 1) | relative | (Default) Scale step size by the parameter value
absolute | Do not scale step-size
bounds | Scale step-size by the domain of the parameter
| Optional (Choose One) | Finite Difference Type (Group 2) | forward | (Default) Use forward differences
central | Use central differences

## Description

The `numerical_hessians` specification means that Hessian information is needed and will be computed with finite differences using either first-order gradient differencing (for the cases of `analytic_gradients` or for the functions identified by `id_analytic_gradients` in the case of `mixed_gradients`) or first- or second-order function value differencing (all other gradient specifications). In the former case, the following expression

estimates the Hessian column, and in the latter case, the following expressions

and

provide first- and second-order estimates of the Hessian term. Prior to Dakota 5.0, Dakota always used second-order estimates. In Dakota 5.0 and newer, the default is to use first-order estimates (which honor bounds on the variables and require only about a quarter as many function evaluations as do the second-order estimates), but specifying `central` after `numerical_hessians` causes Dakota to use the old second-order estimates, which do not honor bounds. In optimization algorithms that use Hessians, there is little reason to use second-order differences in computing Hessian approximations.

## See Also

These keywords may also be of interest:

- no_hessians
- quasi_hessians
- analytic_hessians
- mixed_hessians