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https://issues.apache.org/jira/browse/MATH-867?page=com.atlassian.jira.plugin.system.issuetabpanels:comment-tabpanel&focusedCommentId=13467764#comment-13467764
 ] 

Nikolaus Hansen commented on MATH-867:
--------------------------------------

{quote}
And I have no idea how to improve the documentation...
{quote}

Here are my suggestions: Replace (several times) 
{code}
     * @param inputSigma Initial search volume; sigma of offspring objective 
variables.
{code}
with 

{code}
     * @param inputSigma Initial standard deviations to sample new points from 
startPoint
{code}

and

{code}
    /**
     * Individual sigma values - initial search volume. inputSigma determines
     * the initial coordinate wise standard deviations for the search. Setting
     * SIGMA one third of the initial search region is appropriate.
     */
{code}

with 

{code}
    /**
     * Values in inputSigma define the initial coordinate-wise 
     * standard deviations for sampling new search points about 
     * startPoint. 
     * Setting inputSigma roughly to the predicted distance of 
     * startPoint to the actually desired optimum is appropriate. 
     * Small values for inputSigma induce the search to be more local
     * and very small values are more likely to find a local optimum 
     * close to startPoint. 
     * Extremely small values will however lead to early termination. 
     */
{code}

                
> 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
>             Fix For: 3.1
>
>         Attachments: MATH867_patch, 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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