Dakota Reference Manual  Version 6.4
Large-Scale Engineering Optimization and Uncertainty Analysis
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Description of the model output data returned to Dakota upon evaluation of an interface.


This keyword is related to the topics:


Alias: none

Argument(s): none

Required/Optional Description of Group Dakota Keyword Dakota Keyword Description
Optional id_responses

Name the responses block; helpful when there are multiple

Optional descriptors

Labels for the responses

(Choose One)
response type (Group 1) objective_functions

Response type suitable for optimization


Response type suitable for calibration or least squares


Generic response type

(Choose One)
gradient type (Group 2) no_gradients

Gradients will not be used


Analysis driver will return gradients


Gradients are needed and will be obtained from a mix of numerical and analytic sources


Gradients are needed and will be approximated by finite differences

(Choose One)
Hessian type (Group 3) no_hessians

Hessians will not be used


Hessians are needed and will be approximated by finite differences


Hessians are needed and will be approximated by secant updates (BFGS or SR1) from a series of gradient evaluations


Hessians are needed and are available directly from the analysis driver


Hessians are needed and will be obtained from a mix of numerical, analytic, and "quasi" sources


The responses specification in a Dakota input file indicates the types of data that can be returned by an interface when invoked during Dakota's execution. The specification includes three groups and two optional keywords.

The response type groupindicates the type and number of responses expected by Dakota. It must be one of three types:

  1. Optimization: objective and constraint functions
  2. Calibration: calibration (least squares) terms and constraint functions
  3. Uncertainty Quantifiation: generic response functions

The response type specified should be consistent with the iterative technique called for in the method specification. Certain general-purpose iterative techniques, such as parameter studies and design of experiments methods, can be used with any of these response types.

The gradient type group indicates the availability of first derivatives (gradient vectors) for the response functions.

The gradient specification also links back to the iterative method used. Gradients commonly are needed when the iterative study involves gradient-based optimization, local reliability analysis for uncertainty quantification, or local sensitivity analysis. They can optionally be used to build some types of surrogate models.

The Hessian type group specifies the availability of second derivatives (Hessian matrices) for the response functions.

Hessian availability for the response functions is similar to the gradient availability specifications, with the addition of support for "quasi-Hessians". The Hessian specification also links back to the iterative method in use; Hessians commonly would be used in gradient-based optimization by full Newton methods or in reliability analysis with second-order limit state approximations or second-order probability integrations.


Several examples follow. The first example shows an optimization data set containing an objective function and two nonlinear inequality constraints. These three functions have analytic gradient availability and no Hessian availability.

  objective_functions = 1
    nonlinear_inequality_constraints = 2

The next example shows a typical specification for a calibration data set. The six residual functions will have numerical gradients computed using the dakota finite differencing routine with central differences of 0.1% (plus/minus delta relative to current variables value = .001*value).

  calibration_terms = 6
    method_source dakota
    interval_type central
    fd_gradient_step_size = .001

The last example shows a generic specification that could be used with a nondeterministic sampling iterator. The three response functions have no gradient or Hessian availability; therefore, only function values will be used by the iterator.

  response_functions = 3

Parameter study and design of experiments iterators are not restricted in terms of the response data sets which may be catalogued; they may be used with any of the function specification examples shown above.


Responses specify the total data set that is available for use by the method over the course of iteration. This is distinguished from the data subset described by an active set vector (see Dakota File Data Formats in the Users Manual [Adams et al., 2010]) indicating the particular subset of the response data needed for a particular function evaluation. Thus, the responses specification is a broad description of the data to be used during a study whereas the active set vector indicates the subset currently needed.