<HTML xmlns="http://www.w3.org/TR/REC-html40" xmlns:m="http://schemas.microsoft.com/office/2004/12/omml" xmlns:o="urn:schemas-microsoft-com:office:office" xmlns:v="urn:schemas-microsoft-com:vml" xmlns:w="urn:schemas-microsoft-com:office:word"><head><META content="text/html; charset=us-ascii" http-equiv="Content-Type">
<META content="text/html; charset=us-ascii" HTTP-EQUIV="Content-Type"><meta content="Microsoft Word 14 (filtered medium)" name=Generator><style><!--
/* Font Definitions */
@font-face
{font-family:Wingdings;
panose-1:5 0 0 0 0 0 0 0 0 0;}
@font-face
{font-family:Wingdings;
panose-1:5 0 0 0 0 0 0 0 0 0;}
@font-face
{font-family:Calibri;
panose-1:2 15 5 2 2 2 4 3 2 4;}
/* Style Definitions */
p.MsoNormal, li.MsoNormal, div.MsoNormal
{margin:0cm;
margin-bottom:.0001pt;
font-size:11.0pt;
font-family:"Calibri","sans-serif";
mso-fareast-language:EN-US;}
a:link, span.MsoHyperlink
{mso-style-priority:99;
color:blue;
text-decoration:underline;}
a:visited, span.MsoHyperlinkFollowed
{mso-style-priority:99;
color:purple;
text-decoration:underline;}
p.MsoListParagraph, li.MsoListParagraph, div.MsoListParagraph
{mso-style-priority:34;
margin-top:0cm;
margin-right:0cm;
margin-bottom:0cm;
margin-left:36.0pt;
margin-bottom:.0001pt;
font-size:11.0pt;
font-family:"Calibri","sans-serif";
mso-fareast-language:EN-US;}
span.EmailStyle17
{mso-style-type:personal-compose;
font-family:"Calibri","sans-serif";
color:windowtext;}
.MsoChpDefault
{mso-style-type:export-only;
font-family:"Calibri","sans-serif";
mso-fareast-language:EN-US;}
@page WordSection1
{size:612.0pt 792.0pt;
margin:72.0pt 90.0pt 72.0pt 90.0pt;}
div.WordSection1
{page:WordSection1;}
/* List Definitions */
@list l0
{mso-list-id:58793802;
mso-list-type:hybrid;
mso-list-template-ids:1299741468 105546324 269025283 269025285 269025281 269025283 269025285 269025281 269025283 269025285;}
@list l0:level1
{mso-level-number-format:bullet;
mso-level-text:-;
mso-level-tab-stop:none;
mso-level-number-position:left;
text-indent:-18.0pt;
font-family:"Calibri","sans-serif";
mso-fareast-font-family:Calibri;
mso-bidi-font-family:"Times New Roman";}
@list l0:level2
{mso-level-number-format:bullet;
mso-level-text:o;
mso-level-tab-stop:none;
mso-level-number-position:left;
text-indent:-18.0pt;
font-family:"Courier New";}
@list l0:level3
{mso-level-number-format:bullet;
mso-level-text:\F0A7;
mso-level-tab-stop:none;
mso-level-number-position:left;
text-indent:-18.0pt;
font-family:Wingdings;}
@list l0:level4
{mso-level-number-format:bullet;
mso-level-text:\F0B7;
mso-level-tab-stop:none;
mso-level-number-position:left;
text-indent:-18.0pt;
font-family:Symbol;}
@list l0:level5
{mso-level-number-format:bullet;
mso-level-text:o;
mso-level-tab-stop:none;
mso-level-number-position:left;
text-indent:-18.0pt;
font-family:"Courier New";}
@list l0:level6
{mso-level-number-format:bullet;
mso-level-text:\F0A7;
mso-level-tab-stop:none;
mso-level-number-position:left;
text-indent:-18.0pt;
font-family:Wingdings;}
@list l0:level7
{mso-level-number-format:bullet;
mso-level-text:\F0B7;
mso-level-tab-stop:none;
mso-level-number-position:left;
text-indent:-18.0pt;
font-family:Symbol;}
@list l0:level8
{mso-level-number-format:bullet;
mso-level-text:o;
mso-level-tab-stop:none;
mso-level-number-position:left;
text-indent:-18.0pt;
font-family:"Courier New";}
@list l0:level9
{mso-level-number-format:bullet;
mso-level-text:\F0A7;
mso-level-tab-stop:none;
mso-level-number-position:left;
text-indent:-18.0pt;
font-family:Wingdings;}
ol
{margin-bottom:0cm;}
ul
{margin-bottom:0cm;}
--></style><!--[if gte mso 9]><xml>
<o:shapedefaults v:ext="edit" spidmax="1026" />
</xml><![endif]--><!--[if gte mso 9]><xml>
<o:shapelayout v:ext="edit">
<o:idmap v:ext="edit" data="1" />
</o:shapelayout></xml><![endif]--></head><BODY>
<DIV><div class=WordSection1><p class=MsoNormal>Hello,<o:p></o:p></p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal>I’m trying to solve a problem with a special structure like this one:<o:p></o:p></p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal>Min f(x) + g(y)<o:p></o:p></p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal>Subject to cmin <= c(x,y)<=cmax<o:p></o:p></p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal>x contains most of the decision variables (approx. 15000)<o:p></o:p></p><p class=MsoNormal>y contains only few variable (approx. 10)<o:p></o:p></p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal>function f(x) will return a number in the range [500 2000] whereas g(y) return a number in a completely different range [ around 30.0 e7].<o:p></o:p></p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal>When I try to solve the problem Ipopt finished with ApplicationReturnStatus = 2 (Infeasible_Problem_Detected).<o:p></o:p></p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal>But If I simply scale g(y) in my objective function like this: Min f(x) + g(y)/100000 Ipopt Is able to solve the problem ApplicationReturnStatus = 0.<o:p></o:p></p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal>I suspected of an error in the derivative of g(y) but the derivative check passed (with a tolerance 1.e-6, may be is not enough?). <o:p></o:p></p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal>Does anyone have an idea of what goes wrong.<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><o:p> </o:p></p><p class=MsoListParagraph style='text-indent:-18.0pt;mso-list:l0 level1 lfo1'><![if !supportLists]><span lang=FR-CA><span style='mso-list:Ignore'>-<span style='font:7.0pt "Times New Roman"'> </span></span></span><![endif]>Pascal<span lang=FR-CA><o:p></o:p></span></p></div></DIV>
<DIV><BR>Avis:<BR>Ce message et toute pièce jointe sont la propriété de Rio Tinto et sont destinés seulement aux personnes ou à l'entité à qui le message est adressé. Si vous avez reçu ce message par erreur, veuillez le détruire et en aviser l'expéditeur par courriel. Si vous n'êtes pas le destinataire du message, vous n'êtes pas autorisé à utiliser, à copier ou à divulguer le contenu du message ou ses pièces jointes en tout ou en partie.</DIV>
<DIV> </DIV>
<DIV>Notice:<BR>This message and any attachments are the property of Rio Tinto and are intended solely for the named recipients or entity to whom this message is addressed. If you have received this message in error please inform the sender via e-mail and destroy the message. If you are not the intended recipient you are not allowed to use, copy or disclose the contents or attachments in whole or in part.</DIV></BODY></HTML>