[Ipopt] Question concerning presence of indefinite terms in function

[Daniel Feenberg]

On Tue, 28 Nov 2017, Maxime Boulay wrote:

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> Hello,
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> I am using ipopt to solve an objective function which contains an expression of the form
> x*log(x/(a+x)). This results in a derivative of the form log(x/(a+x)) and a second derivative of the
> form a/(x*(x+a)) when considering other terms in the function. Since this will lead to problems
> whenever x = 0 or x < 0, I am not sure about the best way to treat those cases. I have tried equating
> the expression to 0 whenever those cases are met but this seems wrong since the expression doesn’t
> tend to 0 when approaching the critical values. This also seems to slow down the time taken to find a
> solution whenever the initial values given or the solution include an x=0.

I hesitate to respond, since I am a rank beginner at IPOPT, but no one 
else has, so I will risk embarrassment. The Fortran example program in the 
package shows how to set limits on the x values (see X_L and X_U), and in 
my limited experience, these are respected. Am I missing something?

> Given the fact that many of these may pop out since the function includes a summation, what would be
> the most efficient and correct way to deal with this?

"pop out"?

Daniel Feenberg

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> Thank you.
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