# objective_functions

Response type suitable for optimization

**Specification**

*Alias:*num_objective_functions*Arguments:*INTEGER

**Child Keywords:**

Required/Optional |
Description of Group |
Dakota Keyword |
Dakota Keyword Description |
---|---|---|---|

Optional |
Whether to minimize or maximize each objective function |
||

Optional |
How to scale each objective function |
||

Optional |
Characteristic values to scale each objective function |
||

Optional |
Specify weights for each objective function |
||

Optional |
Group to specify nonlinear inequality constraints |
||

Optional |
Group to specify nonlinear equality constraints |
||

Optional |
Number of scalar objective functions |
||

Optional |
Number of field objective functions |

**Description**

Specifies the number (1 or more) of objective functions \(f_j\) returned to Dakota for use in the general optimization problem formulation:

Unless `sense`

is specified, Dakota
will minimize the objective functions.

The keywords
`nonlinear_inequality_constraints`

and
`nonlinear_equality_constraints`

specify the number of nonlinear inequality constraints *g*, and nonlinear
equality constraints *h*, respectively. When interfacing to external
applications, the responses must be returned to Dakota in this order
in the `results_file`

:

objective functions

nonlinear_inequality_constraints

nonlinear_equality_constraints

An optimization problem’s linear constraints are provided to the
solver at startup only and do not need to be included in the data
returned on every function evaluation. Linear constraints are
therefore specified in the `variables`

block through the
`linear_inequality_constraint_matrix`

\(A_i\) and
`linear_equality_constraint_matrix`

\(A_e\) .

Lower and upper bounds on the design variables *x* are also
specified in the `variables`

block.

The optional keywords relate to scaling the objective functions (for
better numerical results), formulating the problem as minimization or
maximization, and dealing with multiple objective functions through
`weights`

*w*. If scaling is used,
it is applied before multi-objective weighted sums are formed, so,
e.g, when both weighting and characteristic value scaling are present
the ultimate objective function would be: