Dakota Reference Manual  Version 6.4
Large-Scale Engineering Optimization and Uncertainty Analysis
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linear_inequality_scale_types


Specify how each linear inequality constraint is scaled

Topics

This keyword is related to the topics:

Specification

Alias: none

Argument(s): STRINGLIST

Default: vector values = "none"

Description

linear_inequality_scale_types provide strings specifying the scaling type for each linear inequality constraint, in methods that support scaling.

An entry may be selected for each constraint. The options are:

  • 'none' - no scaling
  • 'value' - characteristic value if this is chosen, then linear_inequality_scales must be specified
  • 'auto' - automatic scaling If a single string is specified it will apply to all constraints.

Scaling for linear constraints is applied after any continuous variable scaling. For example, for variable scaling on continuous design variables x:

\[ \tilde{x}^j = \frac{x^j - x^j_O}{x^j_M} \]

we have the following system for linear inequality constraints

\[ a_L \leq A_i x \leq a_U \]

\[ a_L \leq A_i \left( \mathrm{diag}(x_M) \tilde{x} + x_O \right) \leq a_U \]

\[ a_L - A_i x_O \leq A_i \mathrm{diag}(x_M) \tilde{x} \leq a_U - A_i x_O \]

\[ \tilde{a}_L \leq \tilde{A}_i \tilde{x} \leq \tilde{a}_U \]

and user-specified or automatically computed scaling multipliers are appplied to this final transformed system, which accounts for continuous design variable scaling. When automatic scaling is in use for linear constraints they are linearly scaled by a computed characteristic value, but not affinely to [0,1].