<html 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=utf-8">
<meta name="Generator" content="Microsoft Word 15 (filtered medium)">
<style><!--
/* Font Definitions */
@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:"Times New Roman \(Body CS\)";
panose-1:2 11 6 4 2 2 2 2 2 4;}
/* Style Definitions */
p.MsoNormal, li.MsoNormal, div.MsoNormal
{margin:0in;
font-size:11.0pt;
font-family:"Calibri",sans-serif;}
a:link, span.MsoHyperlink
{mso-style-priority:99;
color:blue;
text-decoration:underline;}
span.apple-converted-space
{mso-style-name:apple-converted-space;}
span.EmailStyle19
{mso-style-type:personal-reply;
font-family:"Times New Roman",serif;
color:windowtext;}
.MsoChpDefault
{mso-style-type:export-only;
font-size:10.0pt;}
@page WordSection1
{size:8.5in 11.0in;
margin:1.0in 1.0in 1.0in 1.0in;}
div.WordSection1
{page:WordSection1;}
--></style>
</head>
<body lang="EN-US" link="blue" vlink="purple">
<div class="WordSection1">
<p class="MsoNormal"><span style="font-size:12.0pt;font-family:"Times New Roman",serif">Hi Pierre,<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:12.0pt;font-family:"Times New Roman",serif"> We have not tested PDIPM without equality (or inequality) constraints. I’ll take a look at this over the weekend.
<o:p></o:p></span></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"><span style="font-size:12.0pt;font-family:"Times New Roman",serif">This is the first version of PDIPM and there are many bells and whistles that need to be added before making PDIPM fully functional for solving large problems. We’ve internally
discussed the different pieces needed to make it robust, but we haven’t had time to work on it yet.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:12.0pt;font-family:"Times New Roman",serif"><o:p> </o:p></span></p>
<div>
<p class="MsoNormal"><span style="font-size:12.0pt;font-family:"Times New Roman",serif">Thanks,<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:12.0pt;font-family:"Times New Roman",serif">Shri<o:p></o:p></span></p>
</div>
<div style="border:none;border-top:solid #B5C4DF 1.0pt;padding:3.0pt 0in 0in 0in">
<p class="MsoNormal" style="margin-left:.5in"><b><span style="font-size:12.0pt;color:black">From:
</span></b><span style="font-size:12.0pt;color:black">Pierre Jolivet <pierre.jolivet@enseeiht.fr><br>
<b>Date: </b>Wednesday, August 5, 2020 at 2:11 AM<br>
<b>To: </b>"Abhyankar, Shrirang G" <shrirang.abhyankar@pnnl.gov><br>
<b>Cc: </b>"Dener, Alp" <adener@anl.gov>, PETSc Development <petsc-dev@mcs.anl.gov><br>
<b>Subject: </b>Re: [petsc-dev] TAOPDIPM<o:p></o:p></span></p>
</div>
<div>
<p class="MsoNormal" style="margin-left:.5in"><o:p> </o:p></p>
</div>
<p class="MsoNormal" style="margin-left:.5in">Sorry for these questions, I’m trying to help the said user transitioning from IPOPT over to Tao, and since I’m no expert I run into a bunch of errors myself.<o:p></o:p></p>
<div>
<p class="MsoNormal" style="margin-left:.5in">For example, if I run PDIPM without equality constraint, I now get:<o:p></o:p></p>
</div>
<div>
<p class="MsoNormal" style="margin-left:.5in">[0]PETSC ERROR: VecSet() line 522 in src/vec/vec/interface/rvector.c Null Object: Parameter # 1<o:p></o:p></p>
</div>
<div>
<p class="MsoNormal" style="margin-left:.5in">Indeed, I can see that lambdae is conditionally created line 815, but always used in VecSet() line 522.<o:p></o:p></p>
</div>
<div>
<p class="MsoNormal" style="margin-left:.5in">I think the method is general enough to handle cases without such constraints, and should not thus fail here, right?<o:p></o:p></p>
</div>
<div>
<p class="MsoNormal" style="margin-left:.5in">You should be able to reproduce this by commenting all DE/De/EqualityConstraints/JacobianEquality code from ex1.c.<o:p></o:p></p>
</div>
<div>
<p class="MsoNormal" style="margin-left:.5in"><o:p> </o:p></p>
</div>
<div>
<p class="MsoNormal" style="margin-left:.5in">Thanks,<o:p></o:p></p>
</div>
<div>
<p class="MsoNormal" style="margin-left:.5in">Pierre<o:p></o:p></p>
</div>
<div>
<div>
<p class="MsoNormal" style="margin-left:.5in"><br>
<br>
<o:p></o:p></p>
<blockquote style="margin-top:5.0pt;margin-bottom:5.0pt">
<div>
<p class="MsoNormal" style="margin-left:.5in">On 5 Aug 2020, at 5:27 AM, Abhyankar, Shrirang G <<a href="mailto:shrirang.abhyankar@pnnl.gov">shrirang.abhyankar@pnnl.gov</a>> wrote:<o:p></o:p></p>
</div>
<p class="MsoNormal" style="margin-left:.5in"><o:p> </o:p></p>
<div>
<div>
<p class="MsoNormal" style="margin-left:.5in"><span style="font-size:12.0pt;font-family:"Times New Roman",serif">Pierre,</span><o:p></o:p></p>
</div>
<div>
<p class="MsoNormal" style="margin-left:.5in"><span style="font-size:12.0pt;font-family:"Times New Roman",serif"> Thanks for catching this issue. As Alp pointed out, the issue was because the tolerance was not set correctly.</span><o:p></o:p></p>
</div>
<div>
<p class="MsoNormal" style="margin-left:.5in"><span style="font-size:12.0pt;font-family:"Times New Roman",serif"> </span><o:p></o:p></p>
</div>
<div>
<p class="MsoNormal" style="margin-left:.5in"><span style="font-size:12.0pt;font-family:"Times New Roman",serif">@Alp: Let me know if I can help you with the patch.</span><o:p></o:p></p>
</div>
<div>
<p class="MsoNormal" style="margin-left:.5in"><span style="font-size:12.0pt;font-family:"Times New Roman",serif"> </span><o:p></o:p></p>
</div>
<div>
<div>
<p class="MsoNormal" style="margin-left:.5in"><span style="font-size:12.0pt;font-family:"Times New Roman",serif">Thanks,</span><o:p></o:p></p>
</div>
<div>
<p class="MsoNormal" style="margin-left:.5in"><span style="font-size:12.0pt;font-family:"Times New Roman",serif">Shri </span><o:p></o:p></p>
</div>
</div>
<div>
<p class="MsoNormal" style="margin-left:.5in"><span style="font-size:12.0pt;font-family:"Times New Roman",serif"> </span><o:p></o:p></p>
</div>
<div>
<p class="MsoNormal" style="margin-left:.5in"><span style="font-size:12.0pt;font-family:"Times New Roman",serif"> </span><o:p></o:p></p>
</div>
<div style="border:none;border-top:solid #B5C4DF 1.0pt;padding:3.0pt 0in 0in 0in">
<div style="margin-left:.5in">
<p class="MsoNormal" style="margin-left:.5in"><b><span style="font-size:12.0pt">From:<span class="apple-converted-space"> </span></span></b><span style="font-size:12.0pt">petsc-dev <<a href="mailto:petsc-dev-bounces@mcs.anl.gov">petsc-dev-bounces@mcs.anl.gov</a>>
on behalf of Pierre Jolivet <<a href="mailto:pierre.jolivet@enseeiht.fr">pierre.jolivet@enseeiht.fr</a>><br>
<b>Date:<span class="apple-converted-space"> </span></b>Tuesday, August 4, 2020 at 1:46 PM<br>
<b>To:<span class="apple-converted-space"> </span></b>"Dener, Alp" <<a href="mailto:adener@anl.gov">adener@anl.gov</a>><br>
<b>Cc:<span class="apple-converted-space"> </span></b>PETSc Development <<a href="mailto:petsc-dev@mcs.anl.gov">petsc-dev@mcs.anl.gov</a>><br>
<b>Subject:<span class="apple-converted-space"> </span></b>Re: [petsc-dev] TAOPDIPM</span><o:p></o:p></p>
</div>
</div>
<div>
<div style="margin-left:.5in">
<p class="MsoNormal" style="margin-left:.5in"> <o:p></o:p></p>
</div>
</div>
<div>
<div style="margin-left:.5in">
<p class="MsoNormal" style="margin-left:.5in">Thanks to you both, I’ll forward this to my user.<o:p></o:p></p>
</div>
</div>
<div>
<div style="margin-left:.5in">
<p class="MsoNormal" style="margin-left:.5in">Pierre<o:p></o:p></p>
</div>
</div>
<div>
<div style="margin-left:.5in">
<p class="MsoNormal" style="margin-left:.5in"> <o:p></o:p></p>
</div>
</div>
<blockquote style="border:none;border-left:solid #B5C4DF 4.5pt;padding:0in 0in 0in 4.0pt;margin-left:3.75pt;margin-top:5.0pt;margin-right:0in;margin-bottom:5.0pt" id="MAC_OUTLOOK_ATTRIBUTION_BLOCKQUOTE">
<div>
<div style="margin-left:.5in">
<p class="MsoNormal" style="margin-left:.5in">On 4 Aug 2020, at 7:30 PM, Dener, Alp <<a href="mailto:adener@anl.gov">adener@anl.gov</a>> wrote:<o:p></o:p></p>
</div>
</div>
<div>
<div style="margin-left:.5in">
<p class="MsoNormal" style="margin-left:.5in"> <o:p></o:p></p>
</div>
</div>
<div>
<div style="margin-left:.5in">
<p class="MsoNormal" style="margin-left:.5in">Hi Pierre,<o:p></o:p></p>
</div>
</div>
<div>
<div style="margin-left:.5in">
<p class="MsoNormal" style="margin-left:.5in"> <o:p></o:p></p>
</div>
</div>
<div>
<div style="margin-left:.5in">
<p class="MsoNormal" style="margin-left:.5in">This is indeed an issue with TAO default tolerances.<o:p></o:p></p>
</div>
</div>
<div>
<div style="margin-left:.5in">
<p class="MsoNormal" style="margin-left:.5in"> <o:p></o:p></p>
</div>
</div>
<div>
<div style="margin-left:.5in">
<p class="MsoNormal" style="margin-left:.5in">Specifically it has to do with constraint tolerances. The default value is an exact zero.<o:p></o:p></p>
</div>
</div>
<div>
<div style="margin-left:.5in">
<p class="MsoNormal" style="margin-left:.5in"> <o:p></o:p></p>
</div>
</div>
<div>
<div style="margin-left:.5in">
<p class="MsoNormal" style="margin-left:.5in">The problem should still work with line 89 commented out. Our default gradient tolerance is 1e-8. In your case, commenting out line 90 is causing the solver to try to converge constraints to exact zero and it cannot.<o:p></o:p></p>
</div>
</div>
<div>
<div style="margin-left:.5in">
<p class="MsoNormal" style="margin-left:.5in"> <o:p></o:p></p>
</div>
</div>
<div>
<div style="margin-left:.5in">
<p class="MsoNormal" style="margin-left:.5in">I will get a patch out for this within the week but in the meantime please ensure that the constraint tolerances are set for any constrained problem.<o:p></o:p></p>
</div>
</div>
<div>
<div style="margin-left:.5in">
<p class="MsoNormal" style="margin-left:.5in"> <o:p></o:p></p>
</div>
</div>
<div>
<div style="margin-left:.5in">
<p class="MsoNormal" style="margin-left:.5in">Thank you!<o:p></o:p></p>
</div>
</div>
<div>
<div style="margin-left:.5in">
<p class="MsoNormal" style="margin-left:.5in">—<o:p></o:p></p>
</div>
</div>
<div>
<div style="margin-left:.5in">
<p class="MsoNormal" style="margin-left:.5in">Alp<o:p></o:p></p>
</div>
</div>
<div>
<div style="margin-left:.5in">
<p class="MsoNormal" style="margin-left:.5in"> <o:p></o:p></p>
</div>
</div>
<blockquote style="border:none;border-left:solid #B5C4DF 4.5pt;padding:0in 0in 0in 4.0pt;margin-left:3.75pt;margin-top:5.0pt;margin-right:0in;margin-bottom:5.0pt" id="MAC_OUTLOOK_ATTRIBUTION_BLOCKQUOTE">
<div>
<div style="margin-left:.5in">
<p class="MsoNormal" style="margin-left:.5in">On Aug 4, 2020, at 12:24 PM, Munson, Todd via petsc-dev <<a href="mailto:petsc-dev@mcs.anl.gov">petsc-dev@mcs.anl.gov</a>> wrote:<o:p></o:p></p>
</div>
</div>
<div>
<div style="margin-left:.5in">
<p class="MsoNormal" style="margin-left:.5in"> <o:p></o:p></p>
</div>
</div>
<div>
<div style="margin-left:.5in">
<p class="MsoNormal" style="margin-left:.5in"> <o:p></o:p></p>
</div>
</div>
<div>
<div style="margin-left:.5in">
<p class="MsoNormal" style="margin-left:.5in">Hi Pierre,<o:p></o:p></p>
</div>
</div>
<div>
<div style="margin-left:.5in">
<p class="MsoNormal" style="margin-left:.5in"> <o:p></o:p></p>
</div>
</div>
<div>
<div style="margin-left:.5in">
<p class="MsoNormal" style="margin-left:.5in">I would say the answer to that question is "no, its not expected". <o:p></o:p></p>
</div>
</div>
<div>
<div style="margin-left:.5in">
<p class="MsoNormal" style="margin-left:.5in"> <o:p></o:p></p>
</div>
</div>
<div>
<div style="margin-left:.5in">
<p class="MsoNormal" style="margin-left:.5in">We will look into fixing it. It seems like the default tolerances are being set to zero and the result is an inability to satisfy the constraints or gradient of the Lagrangian to that small of a tolerance.<o:p></o:p></p>
</div>
</div>
<div>
<div style="margin-left:.5in">
<p class="MsoNormal" style="margin-left:.5in"> <o:p></o:p></p>
</div>
</div>
<div>
<div style="margin-left:.5in">
<p class="MsoNormal" style="margin-left:.5in">Thanks for point this out to us! We will get it resolved.<o:p></o:p></p>
</div>
</div>
<div>
<div style="margin-left:.5in">
<p class="MsoNormal" style="margin-left:.5in"> <o:p></o:p></p>
</div>
</div>
<div>
<div style="margin-left:.5in">
<p class="MsoNormal" style="margin-left:.5in">Thanks, Todd.<o:p></o:p></p>
</div>
</div>
<div>
<div style="margin-left:.5in">
<p class="MsoNormal" style="margin-left:.5in"> <o:p></o:p></p>
</div>
</div>
<div>
<div style="margin-left:.5in">
<p class="MsoNormal" style="margin-left:.5in">On 8/4/20, 12:12 PM, "petsc-dev on behalf of Pierre Jolivet" <<a href="mailto:petsc-dev-bounces@mcs.anl.gov">petsc-dev-bounces@mcs.anl.gov</a><span class="apple-converted-space"> </span>on behalf of<span class="apple-converted-space"> </span><a href="mailto:pierre.jolivet@enseeiht.fr">pierre.jolivet@enseeiht.fr</a>>
wrote:<o:p></o:p></p>
</div>
</div>
<div>
<div style="margin-left:.5in">
<p class="MsoNormal" style="margin-left:.5in"> <o:p></o:p></p>
</div>
</div>
<div>
<div style="margin-left:.5in">
<p class="MsoNormal" style="margin-left:.5in"> Hello,<o:p></o:p></p>
</div>
</div>
<div>
<div style="margin-left:.5in">
<p class="MsoNormal" style="margin-left:.5in"> If I comment line 89 and 90 of src/tao/constrained/tutorials/ex1.c from master, the example deadlocks with a single process.<o:p></o:p></p>
</div>
</div>
<div>
<div style="margin-left:.5in">
<p class="MsoNormal" style="margin-left:.5in"> Is this expected?<o:p></o:p></p>
</div>
</div>
<div>
<div style="margin-left:.5in">
<p class="MsoNormal" style="margin-left:.5in"> <o:p></o:p></p>
</div>
</div>
<div>
<div style="margin-left:.5in">
<p class="MsoNormal" style="margin-left:.5in"> Thanks,<o:p></o:p></p>
</div>
</div>
<div>
<div style="margin-left:.5in">
<p class="MsoNormal" style="margin-left:.5in"> Pierre<o:p></o:p></p>
</div>
</div>
<div>
<div style="margin-left:.5in">
<p class="MsoNormal" style="margin-left:.5in"> <o:p></o:p></p>
</div>
</div>
<div>
<div style="margin-left:.5in">
<p class="MsoNormal" style="margin-left:.5in"> $ ./ex1 -tao_monitor<o:p></o:p></p>
</div>
</div>
<div>
<div style="margin-left:.5in">
<p class="MsoNormal" style="margin-left:.5in"> ---- Constrained Problem -----<o:p></o:p></p>
</div>
</div>
<div>
<div style="margin-left:.5in">
<p class="MsoNormal" style="margin-left:.5in"> Solution should be f(1,1)=-2<o:p></o:p></p>
</div>
</div>
<div>
<div style="margin-left:.5in">
<p class="MsoNormal" style="margin-left:.5in"> 0 TAO, Function value: 8., Residual: 8.48528<o:p></o:p></p>
</div>
</div>
<div>
<div style="margin-left:.5in">
<p class="MsoNormal" style="margin-left:.5in"> 1 TAO, Function value: 1.28532, Residual: 10.7411<o:p></o:p></p>
</div>
</div>
<div>
<div style="margin-left:.5in">
<p class="MsoNormal" style="margin-left:.5in"> 2 TAO, Function value: -2.56703, Residual: 1.87847<o:p></o:p></p>
</div>
</div>
<div>
<div style="margin-left:.5in">
<p class="MsoNormal" style="margin-left:.5in"> 3 TAO, Function value: -2.03161, Residual: 0.12881<o:p></o:p></p>
</div>
</div>
<div>
<div style="margin-left:.5in">
<p class="MsoNormal" style="margin-left:.5in"> 4 TAO, Function value: -1.99961, Residual: 0.0450855<o:p></o:p></p>
</div>
</div>
<div>
<div style="margin-left:.5in">
<p class="MsoNormal" style="margin-left:.5in"> 5 TAO, Function value: -1.99993, Residual: 0.000916939<o:p></o:p></p>
</div>
</div>
<div>
<div style="margin-left:.5in">
<p class="MsoNormal" style="margin-left:.5in"> 6 TAO, Function value: -1.99999, Residual: 6.69184e-05<o:p></o:p></p>
</div>
</div>
<div>
<div style="margin-left:.5in">
<p class="MsoNormal" style="margin-left:.5in"> 7 TAO, Function value: -2., Residual: 7.15427e-06<o:p></o:p></p>
</div>
</div>
<div>
<div style="margin-left:.5in">
<p class="MsoNormal" style="margin-left:.5in"> 8 TAO, Function value: -2., Residual: 7.15779e-07<o:p></o:p></p>
</div>
</div>
<div>
<div style="margin-left:.5in">
<p class="MsoNormal" style="margin-left:.5in"> 9 TAO, Function value: -2., Residual: 7.15777e-08<o:p></o:p></p>
</div>
</div>
<div>
<div style="margin-left:.5in">
<p class="MsoNormal" style="margin-left:.5in"> 10 TAO, Function value: -2., Residual: 7.15777e-09<o:p></o:p></p>
</div>
</div>
<div>
<div style="margin-left:.5in">
<p class="MsoNormal" style="margin-left:.5in"> 11 TAO, Function value: -2., Residual: 7.15779e-10<o:p></o:p></p>
</div>
</div>
<div>
<div style="margin-left:.5in">
<p class="MsoNormal" style="margin-left:.5in"> 12 TAO, Function value: -2., Residual: 7.15775e-11<o:p></o:p></p>
</div>
</div>
<div>
<div style="margin-left:.5in">
<p class="MsoNormal" style="margin-left:.5in"> 13 TAO, Function value: -2., Residual: 7.1599e-12<o:p></o:p></p>
</div>
</div>
<div>
<div style="margin-left:.5in">
<p class="MsoNormal" style="margin-left:.5in"> 14 TAO, Function value: -2., Residual: 7.1599e-13<o:p></o:p></p>
</div>
</div>
<div>
<div style="margin-left:.5in">
<p class="MsoNormal" style="margin-left:.5in"> 15 TAO, Function value: -2., Residual: 7.22085e-14<o:p></o:p></p>
</div>
</div>
<div>
<div style="margin-left:.5in">
<p class="MsoNormal" style="margin-left:.5in"> 16 TAO, Function value: -2., Residual: 6.44626e-15<o:p></o:p></p>
</div>
</div>
<div>
<div style="margin-left:.5in">
<p class="MsoNormal" style="margin-left:.5in"> 17 TAO, Function value: -2., Residual: 1.00751e-15<o:p></o:p></p>
</div>
</div>
<div>
<div style="margin-left:.5in">
<p class="MsoNormal" style="margin-left:.5in"> 18 TAO, Function value: -2., Residual: 1.70295e-17<o:p></o:p></p>
</div>
</div>
<div>
<div style="margin-left:.5in">
<p class="MsoNormal" style="margin-left:.5in"> 19 TAO, Function value: -2., Residual: 1.70295e-18<o:p></o:p></p>
</div>
</div>
<div>
<div style="margin-left:.5in">
<p class="MsoNormal" style="margin-left:.5in"> 20 TAO, Function value: -2., Residual: 1.70295e-19<o:p></o:p></p>
</div>
</div>
<div>
<div style="margin-left:.5in">
<p class="MsoNormal" style="margin-left:.5in"> 21 TAO, Function value: -2., Residual: 1.70295e-20<o:p></o:p></p>
</div>
</div>
<div>
<div style="margin-left:.5in">
<p class="MsoNormal" style="margin-left:.5in"> 22 TAO, Function value: -2., Residual: 1.70295e-21<o:p></o:p></p>
</div>
</div>
<div>
<div style="margin-left:.5in">
<p class="MsoNormal" style="margin-left:.5in"> 23 TAO, Function value: -2., Residual: 1.70295e-22<o:p></o:p></p>
</div>
</div>
<div>
<div style="margin-left:.5in">
<p class="MsoNormal" style="margin-left:.5in"> 24 TAO, Function value: -2., Residual: 1.70295e-23<o:p></o:p></p>
</div>
</div>
<div>
<div style="margin-left:.5in">
<p class="MsoNormal" style="margin-left:.5in"> 25 TAO, Function value: -2., Residual: 1.70295e-24<o:p></o:p></p>
</div>
</div>
<div>
<div style="margin-left:.5in">
<p class="MsoNormal" style="margin-left:.5in"> 26 TAO, Function value: -2., Residual: 1.70295e-25<o:p></o:p></p>
</div>
</div>
<div>
<div style="margin-left:.5in">
<p class="MsoNormal" style="margin-left:.5in"> 27 TAO, Function value: -2., Residual: 1.70295e-26<o:p></o:p></p>
</div>
</div>
<div>
<div style="margin-left:.5in">
<p class="MsoNormal" style="margin-left:.5in"> 28 TAO, Function value: -2., Residual: 1.70295e-27<o:p></o:p></p>
</div>
</div>
<div>
<div style="margin-left:.5in">
<p class="MsoNormal" style="margin-left:.5in"> 29 TAO, Function value: -2., Residual: 1.70295e-28<o:p></o:p></p>
</div>
</div>
<div>
<div style="margin-left:.5in">
<p class="MsoNormal" style="margin-left:.5in"> 30 TAO, Function value: -2., Residual: 1.70295e-29<o:p></o:p></p>
</div>
</div>
<div>
<div style="margin-left:.5in">
<p class="MsoNormal" style="margin-left:.5in"> 31 TAO, Function value: -2., Residual: 1.70295e-30<o:p></o:p></p>
</div>
</div>
<div>
<div style="margin-left:.5in">
<p class="MsoNormal" style="margin-left:.5in"> 32 TAO, Function value: -2., Residual: 1.70295e-31<o:p></o:p></p>
</div>
</div>
<div>
<div style="margin-left:.5in">
<p class="MsoNormal" style="margin-left:.5in"> 33 TAO, Function value: -2., Residual: 1.70295e-32<o:p></o:p></p>
</div>
</div>
<div>
<div style="margin-left:.5in">
<p class="MsoNormal" style="margin-left:.5in"> 34 TAO, Function value: -2., Residual: 1.70295e-33<o:p></o:p></p>
</div>
</div>
<div>
<div style="margin-left:.5in">
<p class="MsoNormal" style="margin-left:.5in"> 35 TAO, Function value: -2., Residual: 1.70295e-34<o:p></o:p></p>
</div>
</div>
<div>
<div style="margin-left:.5in">
<p class="MsoNormal" style="margin-left:.5in"> 36 TAO, Function value: -2., Residual: 1.70295e-35<o:p></o:p></p>
</div>
</div>
<div>
<div style="margin-left:.5in">
<p class="MsoNormal" style="margin-left:.5in"> 37 TAO, Function value: -2., Residual: 1.70295e-36<o:p></o:p></p>
</div>
</div>
<div>
<div style="margin-left:.5in">
<p class="MsoNormal" style="margin-left:.5in"> 38 TAO, Function value: -2., Residual: 1.70295e-37<o:p></o:p></p>
</div>
</div>
<div>
<div style="margin-left:.5in">
<p class="MsoNormal" style="margin-left:.5in"> 39 TAO, Function value: -2., Residual: 1.70295e-38<o:p></o:p></p>
</div>
</div>
<div>
<div style="margin-left:.5in">
<p class="MsoNormal" style="margin-left:.5in"> 40 TAO, Function value: -2., Residual: 1.70295e-39<o:p></o:p></p>
</div>
</div>
<div>
<div style="margin-left:.5in">
<p class="MsoNormal" style="margin-left:.5in"> 41 TAO, Function value: -2., Residual: 1.70295e-40<o:p></o:p></p>
</div>
</div>
<div>
<div style="margin-left:.5in">
<p class="MsoNormal" style="margin-left:.5in"> 42 TAO, Function value: -2., Residual: 1.70295e-41<o:p></o:p></p>
</div>
</div>
<div>
<div style="margin-left:.5in">
<p class="MsoNormal" style="margin-left:.5in"> 43 TAO, Function value: -2., Residual: 1.70295e-42<o:p></o:p></p>
</div>
</div>
<div>
<div style="margin-left:.5in">
<p class="MsoNormal" style="margin-left:.5in"> 44 TAO, Function value: -2., Residual: 1.70295e-43<o:p></o:p></p>
</div>
</div>
<div>
<div style="margin-left:.5in">
<p class="MsoNormal" style="margin-left:.5in"> 45 TAO, Function value: -2., Residual: 1.70295e-44<o:p></o:p></p>
</div>
</div>
<div>
<div style="margin-left:.5in">
<p class="MsoNormal" style="margin-left:.5in"> 46 TAO, Function value: -2., Residual: 1.70295e-45<o:p></o:p></p>
</div>
</div>
<div>
<div style="margin-left:.5in">
<p class="MsoNormal" style="margin-left:.5in"> 47 TAO, Function value: -2., Residual: 1.70295e-46<o:p></o:p></p>
</div>
</div>
<div>
<div style="margin-left:.5in">
<p class="MsoNormal" style="margin-left:.5in"> 48 TAO, Function value: -2., Residual: 1.70295e-47<o:p></o:p></p>
</div>
</div>
<div>
<div style="margin-left:.5in">
<p class="MsoNormal" style="margin-left:.5in"> 49 TAO, Function value: -2., Residual: 1.70295e-48<o:p></o:p></p>
</div>
</div>
<div>
<div style="margin-left:.5in">
<p class="MsoNormal" style="margin-left:.5in"> 50 TAO, Function value: -2., Residual: 1.70295e-49<o:p></o:p></p>
</div>
</div>
<div>
<div style="margin-left:.5in">
<p class="MsoNormal" style="margin-left:.5in"> 51 TAO, Function value: -2., Residual: 1.70295e-50<o:p></o:p></p>
</div>
</div>
<div>
<div style="margin-left:.5in">
<p class="MsoNormal" style="margin-left:.5in"> 52 TAO, Function value: -2., Residual: 1.70295e-51<o:p></o:p></p>
</div>
</div>
<div>
<div style="margin-left:.5in">
<p class="MsoNormal" style="margin-left:.5in"> ^C<o:p></o:p></p>
</div>
</div>
</blockquote>
</blockquote>
</div>
</blockquote>
</div>
<p class="MsoNormal" style="margin-left:.5in"><o:p> </o:p></p>
</div>
</div>
</body>
</html>