eldo_user

Optimization
Scaling Design Variables
the scaling problem in computing the differences is eliminated. This corresponds to changing
the design variable to:
where D is a diagonal matrix of scaling.
The Eldo optimizer SQP method uses an affine scaling transformation based on the values of
the upper and lower bounds. If the variable x satisfies the relationship l ≤ x ≤ u, two numbers
can be introduced:
that define the transformation:
With this formula the transformed variable has a range of [-1, 1]. The bounds that correspond to
the change in units must be set on the variable x. The algorithms then operate as if they are
working in the transformed variable space.
When the variables are unbounded below or above, a similar transformation is used by utilizing
the nominal value x 0 . For example, if l = −∞, the transformation is defined as:
When x 0 = u:
A similar transformation is used when u = ∞.
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Eldo® User's Manual, 15.3