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


Define the characteristic values to scale linear equalities

Topics

This keyword is related to the topics:

Specification

Alias: none

Argument(s): REALLIST

Default: vector values = 1 . (no scaling)

Description

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

See the scaling keyword in the method section for details on how to use this keyword.

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].