# [Ipopt] Question concerning presence of indefinite terms in function

Filip Jorissen filip.jorissen at kuleuven.be
Wed Nov 29 04:46:20 EST 2017

```The logarithm of a negative number is undefined, so it does not make sense to evaluate the function for x<=0. So I'd suggest to lower bound x to zero or a small number, assuming that x is an optimisation variable. The function should then not be evaluated for x<=0.

Filip

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Van: Ipopt <ipopt-bounces at coin-or.org> namens Maxime Boulay <mboulay at flogen.com>
Verzonden: dinsdag 28 november 2017 22:26
Aan: Ipopt at list.coin-or.org
CC: RMerdjani at flogen.com
Onderwerp: [Ipopt] Question concerning presence of indefinite terms in function

Hello,

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.

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?

Thank you.

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