<html xmlns:v="urn:schemas-microsoft-com:vml" xmlns:o="urn:schemas-microsoft-com:office:office" xmlns:w="urn:schemas-microsoft-com:office:word" xmlns:m="http://schemas.microsoft.com/office/2004/12/omml" xmlns="http://www.w3.org/TR/REC-html40"><head><meta http-equiv=Content-Type content="text/html; charset=us-ascii"><meta name=Generator content="Microsoft Word 14 (filtered medium)"><style><!--
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</o:shapelayout></xml><![endif]--></head><body lang=EN-US link=blue vlink=purple><div class=WordSection1><p class=MsoNormal>Hello,<o:p></o:p></p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal>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. <o:p></o:p></p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal>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?<o:p></o:p></p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal>Thank you.<o:p></o:p></p><p class=MsoNormal style='text-indent:.5in'><o:p> </o:p></p></div></body></html>