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https://issues.apache.org/jira/browse/MATH-867?page=com.atlassian.jira.plugin.system.issuetabpanels:comment-tabpanel&focusedCommentId=13463747#comment-13463747
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Nikolaus Hansen commented on MATH-867:
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Why are variables transformations generally desirable? Because, for example, if
a parameter x_i should only have positive values, the transformation x_i ->
x_i^2 makes the objective function compatible to any unbounded optimizer. Or,
for example, rescaling of variables (e.g. unit m in km etc) can change an
ill-conditioned problem to a well-conditioned one.
> CMAESOptimizer with bounds fits finely near lower bound and coarsely near
> upper bound.
> ---------------------------------------------------------------------------------------
>
> Key: MATH-867
> URL: https://issues.apache.org/jira/browse/MATH-867
> Project: Commons Math
> Issue Type: Bug
> Reporter: Frank Hess
> Attachments: Math867Test.java
>
>
> When fitting with bounds, the CMAESOptimizer fits finely near the lower bound
> and coarsely near the upper bound. This is because it internally maps the
> fitted parameter range into the interval [0,1]. The unit of least precision
> (ulp) between floating point numbers is much smaller near zero than near one.
> Thus, fits have much better resolution near the lower bound (which is mapped
> to zero) than the upper bound (which is mapped to one). I will attach a
> example program to demonstrate.
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