Dakota Reference Manual  Version 6.4
Large-Scale Engineering Optimization and Uncertainty Analysis
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Define the characteristic values to scale linear inequalities


This keyword is related to the topics:


Alias: none

Argument(s): REALLIST

Default: vector values = 1 . (no scaling)


Each entry in linear_inequality_scales may be a user-specified, nonzero characteristic value to be used in scaling each constraint.

Behavior depends on the choice of linear_inequality_scale_type :

  • scale_type - behavior of linear_inequality_scales
  • 'none' - ignored
  • 'value' - required
  • 'auto' - optional

If a single real value is specified it will apply to all components of the constraint.

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].