 Dakota Reference Manual  Version 6.2 Large-Scale Engineering Optimization and Uncertainty Analysis
scaling

Turn on scaling for variables, responses, and constraints

## Topics

This keyword is related to the topics:

## Specification

Alias: none

Argument(s): none

Default: no scaling

## Description

Some of the optimization and calibration methods support scaling of continuous design variables, objective functions, calibration terms, and constraints. This is activated by by providing the `scaling` keyword. Discrete variable scaling is not supported.

When scaling is enabled, variables, functions, gradients, Hessians, etc., are transformed such that the method iterates in scaled variable space, whereas evaluations of the computational model as specified in the interface are performed on the original problem scale. Therefore using scaling does not require rewriting the interface to the simulation code.

Scaling also requires the specification of additional keywords which are found in the method, variables, and responses blocks. When the `scaling` keyword is omitted, all `_scale_types` and `*_scales` specifications are ignored in the method, variables, and responses sections.

This page describes the usage of all scaling related keywords. The additional keywords come in pairs, one pair for each set of quantities to be scaled. These quantities can be constraint equations, variables, or responses.

• a `*scales` keyword, which gives characteristic values
• a `*scale_type` keyword, which determines how to use the characteristic values

The pair of keywords both take argument(s), and the length of the arguments can either be zero, one, or equal to the number of quantities to be scaled. If one argument is given, it will apply to all quantities in the set. See the examples below.

Scale Types

There are four scale types:

1. `none` (default) - no scaling, value of `*scales` keyword is ignored
2. `value` - multiplicative scaling
3. `auto` - automatic scaling

First the quantity is scaled by the characteristic value, then automatic scaling will be attempted according to the following scheme:

• two-sided bounds scaled into the interval [0,1];
• one-sided bound or targets are scaled by the characteristic value, moving the bound or target to 1 and changing the sense of inequalities where necessary;
• no bounds or targets: no automatic scaling possible, therefore no scaling for this component

Automatic scaling is not available for objective functions nor calibration terms since they lack bound constraints. Futher, when automatically scaled, linear constraints are scaled by characteristic values only, not affinely scaled into [0,1].

4. `log` - logarithmic scaling

First, any characteristic values from the optional `*_scales` specification are applied. Then logarithm base 10 scaling is applied.

Logarithmic scaling is not available for linear constraints.

When continuous design variables are log scaled, linear constraints are not allowed.

Scales

The `*scales` keywords are used to specify the characteristic values. These must be non-zero real numbers. The numbers are used according to the corresponding `*scale_type`, as described above.

Depending on the scale type, the characteristic values may be required or optional.

• `none`, `auto`, `log` - optional
• `value` - required.

A warning is issued if scaling would result in division by a value smaller in magnitude than `1.0e10*DBL_MIN`. User-provided values violating this lower bound are accepted unaltered, whereas for automatically calculated scaling, the lower bound is enforced.

## Examples

The two examples below are equivalent:

```  responses
objective_functions 3
sense "maximize"
primary_scale_types = "value"
primary_scales = 1 1 100
```
```  responses
objective_functions 3
sense "maximize"
primary_scale_types = "value" "value" "value"
primary_scales = 1 1 100
```