<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)">
<!--[if !mso]><style>v\:* {behavior:url(#default#VML);}
o\:* {behavior:url(#default#VML);}
w\:* {behavior:url(#default#VML);}
.shape {behavior:url(#default#VML);}
</style><![endif]--><style><!--
/* Font Definitions */
@font-face
{font-family:\5B8B\4F53;
panose-1:2 1 6 0 3 1 1 1 1 1;}
@font-face
{font-family:"Cambria Math";
panose-1:2 4 5 3 5 4 6 3 2 4;}
@font-face
{font-family:Calibri;
panose-1:2 15 5 2 2 2 4 3 2 4;}
@font-face
{font-family:Tahoma;
panose-1:2 11 6 4 3 5 4 4 2 4;}
@font-face
{font-family:"\@\5B8B\4F53";
panose-1:2 1 6 0 3 1 1 1 1 1;}
/* Style Definitions */
p.MsoNormal, li.MsoNormal, div.MsoNormal
{margin:0cm;
margin-bottom:.0001pt;
font-size:11.0pt;
font-family:"Calibri","sans-serif";}
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.MsoAcetate, li.MsoAcetate, div.MsoAcetate
{mso-style-priority:99;
mso-style-link:"Balloon Text Char";
margin:0cm;
margin-bottom:.0001pt;
font-size:8.0pt;
font-family:"Tahoma","sans-serif";}
span.EmailStyle17
{mso-style-type:personal-compose;
font-family:"Calibri","sans-serif";
color:windowtext;}
span.BalloonTextChar
{mso-style-name:"Balloon Text Char";
mso-style-priority:99;
mso-style-link:"Balloon Text";
font-family:"Tahoma","sans-serif";}
.MsoChpDefault
{mso-style-type:export-only;
font-family:"Calibri","sans-serif";}
@page WordSection1
{size:612.0pt 792.0pt;
margin:72.0pt 90.0pt 72.0pt 90.0pt;}
div.WordSection1
{page:WordSection1;}
--></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 lang="EN-GB" link="blue" vlink="purple">
<div class="WordSection1">
<p class="MsoNormal">Hi everyone,<o:p></o:p></p>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal">I used IPOPT to solve a nonlinear problem and get an optimal solution<!--[if gte msEquation 12]><m:oMath><m:sSup><m:sSupPr><span style='font-family:"Cambria Math","serif";font-style:italic'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><i><span style='font-family:"Cambria Math","serif"'><m:r>x</m:r></span></i></m:e><m:sup><i><span style='font-family:"Cambria Math","serif"'><m:r>*</m:r></span></i></m:sup></m:sSup><i><span style='font-family:"Cambria Math","serif"'><m:r>∈</m:r></span></i><m:sSup><m:sSupPr><span style='font-family:"Cambria Math","serif";font-style:italic'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><i><span style='font-family:"Cambria Math","serif"'><m:r><m:rPr><m:scr m:val="fraktur"/><m:sty m:val="i"/></m:rPr>R</m:r></span></i></m:e><m:sup><i><span style='font-family:"Cambria Math","serif"'><m:r>n</m:r><m:r>×1</m:r></span></i></m:sup></m:sSup></m:oMath><![endif]--><![if !msEquation]>
<span style="font-size:11.0pt;font-family:"Calibri","sans-serif";position:relative;top:2.5pt;mso-text-raise:-2.5pt;mso-fareast-language:ZH-CN">
<img width="64" height="17" id="_x0000_i1025" src="cid:image001.png@01D0670A.F58851B0"></span><![endif]>. But it goes wrong when I attempted to add another linear constraint<!--[if gte msEquation 12]><m:oMath><i><span style='font-family:"Cambria Math","serif"'><m:r>Ax</m:r><m:r>=</m:r><m:r>b</m:r></span></i></m:oMath><![endif]--><![if !msEquation]>
<span style="font-size:11.0pt;font-family:"Calibri","sans-serif";position:relative;top:2.5pt;mso-text-raise:-2.5pt;mso-fareast-language:ZH-CN">
<img width="45" height="17" id="_x0000_i1025" src="cid:image002.png@01D0670A.F58851B0"></span><![endif]> to the original problem, where<!--[if gte msEquation 12]><m:oMath><i><span style='font-family:"Cambria Math","serif"'><m:r>A</m:r></span></i><m:sSup><m:sSupPr><span style='font-family:"Cambria Math","serif";font-style:italic'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><i><span style='font-family:"Cambria Math","serif"'><m:r>x</m:r></span></i></m:e><m:sup><i><span style='font-family:"Cambria Math","serif"'><m:r>*</m:r></span></i></m:sup></m:sSup><i><span style='font-family:"Cambria Math","serif"'><m:r>=</m:r><m:r>b</m:r></span></i></m:oMath><![endif]--><![if !msEquation]>
<span style="font-size:11.0pt;font-family:"Calibri","sans-serif";position:relative;top:2.5pt;mso-text-raise:-2.5pt;mso-fareast-language:ZH-CN">
<img width="51" height="17" id="_x0000_i1025" src="cid:image003.png@01D0670A.F58851B0"></span><![endif]> still holds. The error message is ‘Problem has too few degrees of freedom’ even the optimal solution<!--[if gte msEquation 12]><m:oMath><m:sSup><m:sSupPr><span style='font-family:"Cambria Math","serif";font-style:italic'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><i><span style='font-family:"Cambria Math","serif"'><m:r>x</m:r></span></i></m:e><m:sup><i><span style='font-family:"Cambria Math","serif"'><m:r>*</m:r></span></i></m:sup></m:sSup></m:oMath><![endif]--><![if !msEquation]>
<span style="font-size:11.0pt;font-family:"Calibri","sans-serif";position:relative;top:2.5pt;mso-text-raise:-2.5pt;mso-fareast-language:ZH-CN">
<img width="14" height="17" id="_x0000_i1025" src="cid:image004.png@01D0670A.F58851B0"></span><![endif]> is provided as initial searching point. I wonder whether this is because IPOPT would check the degrees of freedom first then begin to search? Otherwise
it could just end up with the initial searching point provided as it is the solution that satisfies all the constraints. Please advise.
<o:p></o:p></p>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal">Many thanks<o:p></o:p></p>
<p class="MsoNormal"><span style="font-size:12.0pt;font-family:"Times New Roman","serif""><o:p> </o:p></span></p>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal">Steve<o:p></o:p></p>
<p class="MsoNormal"><o:p> </o:p></p>
</div>
</body>
</html>