<html><head><meta http-equiv="Content-Type" content="text/html; charset=utf-8"></head><body style="word-wrap: break-word; -webkit-nbsp-mode: space; line-break: after-white-space;" class="">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.<div class="">For example, if I run PDIPM without equality constraint, I now get:</div><div class="">[0]PETSC ERROR: VecSet() line 522 in src/vec/vec/interface/rvector.c Null Object: Parameter # 1</div><div class="">Indeed, I can see that lambdae is conditionally created line 815, but always used in VecSet() line 522.</div><div class="">I think the method is general enough to handle cases without such constraints, and should not thus fail here, right?</div><div class="">You should be able to reproduce this by commenting all DE/De/EqualityConstraints/JacobianEquality code from ex1.c.</div><div class=""><br class=""></div><div class="">Thanks,</div><div class="">Pierre</div><div class=""><div><br class=""><blockquote type="cite" class=""><div class="">On 5 Aug 2020, at 5:27 AM, Abhyankar, Shrirang G <<a href="mailto:shrirang.abhyankar@pnnl.gov" class="">shrirang.abhyankar@pnnl.gov</a>> wrote:</div><br class="Apple-interchange-newline"><div class=""><div class="WordSection1" style="page: WordSection1; caret-color: rgb(0, 0, 0); font-family: Helvetica; font-size: 12px; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none;"><div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span style="font-size: 12pt; font-family: "Times New Roman", serif;" class="">Pierre,<o:p class=""></o:p></span></div><div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span style="font-size: 12pt; font-family: "Times New Roman", serif;" class=""> Thanks for catching this issue. As Alp pointed out, the issue was because the tolerance was not set correctly.<o:p class=""></o:p></span></div><div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span style="font-size: 12pt; font-family: "Times New Roman", serif;" class=""><o:p class=""> </o:p></span></div><div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span style="font-size: 12pt; font-family: "Times New Roman", serif;" class="">@Alp: Let me know if I can help you with the patch.<o:p class=""></o:p></span></div><div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span style="font-size: 12pt; font-family: "Times New Roman", serif;" class=""><o:p class=""> </o:p></span></div><div class=""><div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span style="font-size: 12pt; font-family: "Times New Roman", serif;" class="">Thanks,<o:p class=""></o:p></span></div><div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span style="font-size: 12pt; font-family: "Times New Roman", serif;" class="">Shri <o:p class=""></o:p></span></div></div><div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span style="font-size: 12pt; font-family: "Times New Roman", serif;" class=""><o:p class=""> </o:p></span></div><div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span style="font-size: 12pt; font-family: "Times New Roman", serif;" class=""><o:p class=""> </o:p></span></div><div style="border-style: solid none none; border-top-width: 1pt; border-top-color: rgb(181, 196, 223); padding: 3pt 0in 0in;" class=""><div style="margin: 0in 0in 0in 0.5in; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><b class=""><span style="font-size: 12pt;" class="">From:<span class="Apple-converted-space"> </span></span></b><span style="font-size: 12pt;" class="">petsc-dev <<a href="mailto:petsc-dev-bounces@mcs.anl.gov" class="">petsc-dev-bounces@mcs.anl.gov</a>> on behalf of Pierre Jolivet <<a href="mailto:pierre.jolivet@enseeiht.fr" class="">pierre.jolivet@enseeiht.fr</a>><br class=""><b class="">Date:<span class="Apple-converted-space"> </span></b>Tuesday, August 4, 2020 at 1:46 PM<br class=""><b class="">To:<span class="Apple-converted-space"> </span></b>"Dener, Alp" <<a href="mailto:adener@anl.gov" class="">adener@anl.gov</a>><br class=""><b class="">Cc:<span class="Apple-converted-space"> </span></b>PETSc Development <<a href="mailto:petsc-dev@mcs.anl.gov" class="">petsc-dev@mcs.anl.gov</a>><br class=""><b class="">Subject:<span class="Apple-converted-space"> </span></b>Re: [petsc-dev] TAOPDIPM<o:p class=""></o:p></span></div></div><div class=""><div style="margin: 0in 0in 0in 0.5in; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><o:p class=""> </o:p></div></div><div class=""><div style="margin: 0in 0in 0in 0.5in; font-size: 11pt; font-family: Calibri, sans-serif;" class="">Thanks to you both, I’ll forward this to my user.<o:p class=""></o:p></div></div><div class=""><div style="margin: 0in 0in 0in 0.5in; font-size: 11pt; font-family: Calibri, sans-serif;" class="">Pierre<o:p class=""></o:p></div></div><div class=""><div style="margin: 0in 0in 0in 0.5in; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><o:p class=""> </o:p></div></div><blockquote id="MAC_OUTLOOK_ATTRIBUTION_BLOCKQUOTE" style="border-style: none none none solid; border-left-width: 4.5pt; border-left-color: rgb(181, 196, 223); padding: 0in 0in 0in 4pt; margin-left: 3.75pt; margin-right: 0in;" class="" type="cite"><div class=""><div style="margin: 0in 0in 0in 0.5in; font-size: 11pt; font-family: Calibri, sans-serif;" class="">On 4 Aug 2020, at 7:30 PM, Dener, Alp <<a href="mailto:adener@anl.gov" style="color: blue; text-decoration: underline;" class="">adener@anl.gov</a>> wrote:<o:p class=""></o:p></div></div><div class=""><div style="margin: 0in 0in 0in 0.5in; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><o:p class=""> </o:p></div></div><div class=""><div style="margin: 0in 0in 0in 0.5in; font-size: 11pt; font-family: Calibri, sans-serif;" class="">Hi Pierre,<o:p class=""></o:p></div></div><div class=""><div style="margin: 0in 0in 0in 0.5in; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><o:p class=""> </o:p></div></div><div class=""><div style="margin: 0in 0in 0in 0.5in; font-size: 11pt; font-family: Calibri, sans-serif;" class="">This is indeed an issue with TAO default tolerances.<o:p class=""></o:p></div></div><div class=""><div style="margin: 0in 0in 0in 0.5in; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><o:p class=""> </o:p></div></div><div class=""><div style="margin: 0in 0in 0in 0.5in; font-size: 11pt; font-family: Calibri, sans-serif;" class="">Specifically it has to do with constraint tolerances. The default value is an exact zero.<o:p class=""></o:p></div></div><div class=""><div style="margin: 0in 0in 0in 0.5in; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><o:p class=""> </o:p></div></div><div class=""><div style="margin: 0in 0in 0in 0.5in; font-size: 11pt; font-family: Calibri, sans-serif;" class="">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 class=""></o:p></div></div><div class=""><div style="margin: 0in 0in 0in 0.5in; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><o:p class=""> </o:p></div></div><div class=""><div style="margin: 0in 0in 0in 0.5in; font-size: 11pt; font-family: Calibri, sans-serif;" class="">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 class=""></o:p></div></div><div class=""><div style="margin: 0in 0in 0in 0.5in; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><o:p class=""> </o:p></div></div><div class=""><div style="margin: 0in 0in 0in 0.5in; font-size: 11pt; font-family: Calibri, sans-serif;" class="">Thank you!<o:p class=""></o:p></div></div><div class=""><div style="margin: 0in 0in 0in 0.5in; font-size: 11pt; font-family: Calibri, sans-serif;" class="">—<o:p class=""></o:p></div></div><div class=""><div style="margin: 0in 0in 0in 0.5in; font-size: 11pt; font-family: Calibri, sans-serif;" class="">Alp<o:p class=""></o:p></div></div><div class=""><div style="margin: 0in 0in 0in 0.5in; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><o:p class=""> </o:p></div></div><blockquote id="MAC_OUTLOOK_ATTRIBUTION_BLOCKQUOTE" style="border-style: none none none solid; border-left-width: 4.5pt; border-left-color: rgb(181, 196, 223); padding: 0in 0in 0in 4pt; margin-left: 3.75pt; margin-right: 0in;" class="" type="cite"><div class=""><div style="margin: 0in 0in 0in 0.5in; font-size: 11pt; font-family: Calibri, sans-serif;" class="">On Aug 4, 2020, at 12:24 PM, Munson, Todd via petsc-dev <<a href="mailto:petsc-dev@mcs.anl.gov" style="color: blue; text-decoration: underline;" class="">petsc-dev@mcs.anl.gov</a>> wrote:<o:p class=""></o:p></div></div><div class=""><div style="margin: 0in 0in 0in 0.5in; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><o:p class=""> </o:p></div></div><div class=""><div style="margin: 0in 0in 0in 0.5in; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><o:p class=""> </o:p></div></div><div class=""><div style="margin: 0in 0in 0in 0.5in; font-size: 11pt; font-family: Calibri, sans-serif;" class="">Hi Pierre,<o:p class=""></o:p></div></div><div class=""><div style="margin: 0in 0in 0in 0.5in; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><o:p class=""> </o:p></div></div><div class=""><div style="margin: 0in 0in 0in 0.5in; font-size: 11pt; font-family: Calibri, sans-serif;" class="">I would say the answer to that question is "no, its not expected". <o:p class=""></o:p></div></div><div class=""><div style="margin: 0in 0in 0in 0.5in; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><o:p class=""> </o:p></div></div><div class=""><div style="margin: 0in 0in 0in 0.5in; font-size: 11pt; font-family: Calibri, sans-serif;" class="">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 class=""></o:p></div></div><div class=""><div style="margin: 0in 0in 0in 0.5in; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><o:p class=""> </o:p></div></div><div class=""><div style="margin: 0in 0in 0in 0.5in; font-size: 11pt; font-family: Calibri, sans-serif;" class="">Thanks for point this out to us! We will get it resolved.<o:p class=""></o:p></div></div><div class=""><div style="margin: 0in 0in 0in 0.5in; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><o:p class=""> </o:p></div></div><div class=""><div style="margin: 0in 0in 0in 0.5in; font-size: 11pt; font-family: Calibri, sans-serif;" class="">Thanks, Todd.<o:p class=""></o:p></div></div><div class=""><div style="margin: 0in 0in 0in 0.5in; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><o:p class=""> </o:p></div></div><div class=""><div style="margin: 0in 0in 0in 0.5in; font-size: 11pt; font-family: Calibri, sans-serif;" class="">On 8/4/20, 12:12 PM, "petsc-dev on behalf of Pierre Jolivet" <<a href="mailto:petsc-dev-bounces@mcs.anl.gov" style="color: blue; text-decoration: underline;" class="">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" style="color: blue; text-decoration: underline;" class="">pierre.jolivet@enseeiht.fr</a>> wrote:<o:p class=""></o:p></div></div><div class=""><div style="margin: 0in 0in 0in 0.5in; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><o:p class=""> </o:p></div></div><div class=""><div style="margin: 0in 0in 0in 0.5in; font-size: 11pt; font-family: Calibri, sans-serif;" class=""> Hello,<o:p class=""></o:p></div></div><div class=""><div style="margin: 0in 0in 0in 0.5in; font-size: 11pt; font-family: Calibri, sans-serif;" class=""> 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 class=""></o:p></div></div><div class=""><div style="margin: 0in 0in 0in 0.5in; font-size: 11pt; font-family: Calibri, sans-serif;" class=""> Is this expected?<o:p class=""></o:p></div></div><div class=""><div style="margin: 0in 0in 0in 0.5in; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><o:p class=""> </o:p></div></div><div class=""><div style="margin: 0in 0in 0in 0.5in; font-size: 11pt; font-family: Calibri, sans-serif;" class=""> Thanks,<o:p class=""></o:p></div></div><div class=""><div style="margin: 0in 0in 0in 0.5in; font-size: 11pt; font-family: Calibri, sans-serif;" class=""> Pierre<o:p class=""></o:p></div></div><div class=""><div style="margin: 0in 0in 0in 0.5in; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><o:p class=""> </o:p></div></div><div class=""><div style="margin: 0in 0in 0in 0.5in; font-size: 11pt; font-family: Calibri, sans-serif;" class=""> $ ./ex1 -tao_monitor<o:p class=""></o:p></div></div><div class=""><div style="margin: 0in 0in 0in 0.5in; font-size: 11pt; font-family: Calibri, sans-serif;" class=""> ---- Constrained Problem -----<o:p class=""></o:p></div></div><div class=""><div style="margin: 0in 0in 0in 0.5in; font-size: 11pt; font-family: Calibri, sans-serif;" class=""> Solution should be f(1,1)=-2<o:p class=""></o:p></div></div><div class=""><div style="margin: 0in 0in 0in 0.5in; font-size: 11pt; font-family: Calibri, sans-serif;" class=""> 0 TAO, Function value: 8., Residual: 8.48528<o:p class=""></o:p></div></div><div class=""><div style="margin: 0in 0in 0in 0.5in; font-size: 11pt; font-family: Calibri, sans-serif;" class=""> 1 TAO, Function value: 1.28532, Residual: 10.7411<o:p class=""></o:p></div></div><div class=""><div style="margin: 0in 0in 0in 0.5in; font-size: 11pt; font-family: Calibri, sans-serif;" class=""> 2 TAO, Function value: -2.56703, Residual: 1.87847<o:p class=""></o:p></div></div><div class=""><div style="margin: 0in 0in 0in 0.5in; font-size: 11pt; font-family: Calibri, sans-serif;" class=""> 3 TAO, Function value: -2.03161, Residual: 0.12881<o:p class=""></o:p></div></div><div class=""><div style="margin: 0in 0in 0in 0.5in; font-size: 11pt; font-family: Calibri, sans-serif;" class=""> 4 TAO, Function value: -1.99961, Residual: 0.0450855<o:p class=""></o:p></div></div><div class=""><div style="margin: 0in 0in 0in 0.5in; font-size: 11pt; font-family: Calibri, sans-serif;" class=""> 5 TAO, Function value: -1.99993, Residual: 0.000916939<o:p class=""></o:p></div></div><div class=""><div style="margin: 0in 0in 0in 0.5in; font-size: 11pt; font-family: Calibri, sans-serif;" class=""> 6 TAO, Function value: -1.99999, Residual: 6.69184e-05<o:p class=""></o:p></div></div><div class=""><div style="margin: 0in 0in 0in 0.5in; font-size: 11pt; font-family: Calibri, sans-serif;" class=""> 7 TAO, Function value: -2., Residual: 7.15427e-06<o:p class=""></o:p></div></div><div class=""><div style="margin: 0in 0in 0in 0.5in; font-size: 11pt; font-family: Calibri, sans-serif;" class=""> 8 TAO, Function value: -2., Residual: 7.15779e-07<o:p class=""></o:p></div></div><div class=""><div style="margin: 0in 0in 0in 0.5in; font-size: 11pt; font-family: Calibri, sans-serif;" class=""> 9 TAO, Function value: -2., Residual: 7.15777e-08<o:p class=""></o:p></div></div><div class=""><div style="margin: 0in 0in 0in 0.5in; font-size: 11pt; font-family: Calibri, sans-serif;" class=""> 10 TAO, Function value: -2., Residual: 7.15777e-09<o:p class=""></o:p></div></div><div class=""><div style="margin: 0in 0in 0in 0.5in; font-size: 11pt; font-family: Calibri, sans-serif;" class=""> 11 TAO, Function value: -2., Residual: 7.15779e-10<o:p class=""></o:p></div></div><div class=""><div style="margin: 0in 0in 0in 0.5in; font-size: 11pt; font-family: Calibri, sans-serif;" class=""> 12 TAO, Function value: -2., Residual: 7.15775e-11<o:p class=""></o:p></div></div><div class=""><div style="margin: 0in 0in 0in 0.5in; font-size: 11pt; font-family: Calibri, sans-serif;" class=""> 13 TAO, Function value: -2., Residual: 7.1599e-12<o:p class=""></o:p></div></div><div class=""><div style="margin: 0in 0in 0in 0.5in; font-size: 11pt; font-family: Calibri, sans-serif;" class=""> 14 TAO, Function value: -2., Residual: 7.1599e-13<o:p class=""></o:p></div></div><div class=""><div style="margin: 0in 0in 0in 0.5in; font-size: 11pt; font-family: Calibri, sans-serif;" class=""> 15 TAO, Function value: -2., Residual: 7.22085e-14<o:p class=""></o:p></div></div><div class=""><div style="margin: 0in 0in 0in 0.5in; font-size: 11pt; font-family: Calibri, sans-serif;" class=""> 16 TAO, Function value: -2., Residual: 6.44626e-15<o:p class=""></o:p></div></div><div class=""><div style="margin: 0in 0in 0in 0.5in; font-size: 11pt; font-family: Calibri, sans-serif;" class=""> 17 TAO, Function value: -2., Residual: 1.00751e-15<o:p class=""></o:p></div></div><div class=""><div style="margin: 0in 0in 0in 0.5in; font-size: 11pt; font-family: Calibri, sans-serif;" class=""> 18 TAO, Function value: -2., Residual: 1.70295e-17<o:p class=""></o:p></div></div><div class=""><div style="margin: 0in 0in 0in 0.5in; font-size: 11pt; font-family: Calibri, sans-serif;" class=""> 19 TAO, Function value: -2., Residual: 1.70295e-18<o:p class=""></o:p></div></div><div class=""><div style="margin: 0in 0in 0in 0.5in; font-size: 11pt; font-family: Calibri, sans-serif;" class=""> 20 TAO, Function value: -2., Residual: 1.70295e-19<o:p class=""></o:p></div></div><div class=""><div style="margin: 0in 0in 0in 0.5in; font-size: 11pt; font-family: Calibri, sans-serif;" class=""> 21 TAO, Function value: -2., Residual: 1.70295e-20<o:p class=""></o:p></div></div><div class=""><div style="margin: 0in 0in 0in 0.5in; font-size: 11pt; font-family: Calibri, sans-serif;" class=""> 22 TAO, Function value: -2., Residual: 1.70295e-21<o:p class=""></o:p></div></div><div class=""><div style="margin: 0in 0in 0in 0.5in; font-size: 11pt; font-family: Calibri, sans-serif;" class=""> 23 TAO, Function value: -2., Residual: 1.70295e-22<o:p class=""></o:p></div></div><div class=""><div style="margin: 0in 0in 0in 0.5in; font-size: 11pt; font-family: Calibri, sans-serif;" class=""> 24 TAO, Function value: -2., Residual: 1.70295e-23<o:p class=""></o:p></div></div><div class=""><div style="margin: 0in 0in 0in 0.5in; font-size: 11pt; font-family: Calibri, sans-serif;" class=""> 25 TAO, Function value: -2., Residual: 1.70295e-24<o:p class=""></o:p></div></div><div class=""><div style="margin: 0in 0in 0in 0.5in; font-size: 11pt; font-family: Calibri, sans-serif;" class=""> 26 TAO, Function value: -2., Residual: 1.70295e-25<o:p class=""></o:p></div></div><div class=""><div style="margin: 0in 0in 0in 0.5in; font-size: 11pt; font-family: Calibri, sans-serif;" class=""> 27 TAO, Function value: -2., Residual: 1.70295e-26<o:p class=""></o:p></div></div><div class=""><div style="margin: 0in 0in 0in 0.5in; font-size: 11pt; font-family: Calibri, sans-serif;" class=""> 28 TAO, Function value: -2., Residual: 1.70295e-27<o:p class=""></o:p></div></div><div class=""><div style="margin: 0in 0in 0in 0.5in; font-size: 11pt; font-family: Calibri, sans-serif;" class=""> 29 TAO, Function value: -2., Residual: 1.70295e-28<o:p class=""></o:p></div></div><div class=""><div style="margin: 0in 0in 0in 0.5in; font-size: 11pt; font-family: Calibri, sans-serif;" class=""> 30 TAO, Function value: -2., Residual: 1.70295e-29<o:p class=""></o:p></div></div><div class=""><div style="margin: 0in 0in 0in 0.5in; font-size: 11pt; font-family: Calibri, sans-serif;" class=""> 31 TAO, Function value: -2., Residual: 1.70295e-30<o:p class=""></o:p></div></div><div class=""><div style="margin: 0in 0in 0in 0.5in; font-size: 11pt; font-family: Calibri, sans-serif;" class=""> 32 TAO, Function value: -2., Residual: 1.70295e-31<o:p class=""></o:p></div></div><div class=""><div style="margin: 0in 0in 0in 0.5in; font-size: 11pt; font-family: Calibri, sans-serif;" class=""> 33 TAO, Function value: -2., Residual: 1.70295e-32<o:p class=""></o:p></div></div><div class=""><div style="margin: 0in 0in 0in 0.5in; font-size: 11pt; font-family: Calibri, sans-serif;" class=""> 34 TAO, Function value: -2., Residual: 1.70295e-33<o:p class=""></o:p></div></div><div class=""><div style="margin: 0in 0in 0in 0.5in; font-size: 11pt; font-family: Calibri, sans-serif;" class=""> 35 TAO, Function value: -2., Residual: 1.70295e-34<o:p class=""></o:p></div></div><div class=""><div style="margin: 0in 0in 0in 0.5in; font-size: 11pt; font-family: Calibri, sans-serif;" class=""> 36 TAO, Function value: -2., Residual: 1.70295e-35<o:p class=""></o:p></div></div><div class=""><div style="margin: 0in 0in 0in 0.5in; font-size: 11pt; font-family: Calibri, sans-serif;" class=""> 37 TAO, Function value: -2., Residual: 1.70295e-36<o:p class=""></o:p></div></div><div class=""><div style="margin: 0in 0in 0in 0.5in; font-size: 11pt; font-family: Calibri, sans-serif;" class=""> 38 TAO, Function value: -2., Residual: 1.70295e-37<o:p class=""></o:p></div></div><div class=""><div style="margin: 0in 0in 0in 0.5in; font-size: 11pt; font-family: Calibri, sans-serif;" class=""> 39 TAO, Function value: -2., Residual: 1.70295e-38<o:p class=""></o:p></div></div><div class=""><div style="margin: 0in 0in 0in 0.5in; font-size: 11pt; font-family: Calibri, sans-serif;" class=""> 40 TAO, Function value: -2., Residual: 1.70295e-39<o:p class=""></o:p></div></div><div class=""><div style="margin: 0in 0in 0in 0.5in; font-size: 11pt; font-family: Calibri, sans-serif;" class=""> 41 TAO, Function value: -2., Residual: 1.70295e-40<o:p class=""></o:p></div></div><div class=""><div style="margin: 0in 0in 0in 0.5in; font-size: 11pt; font-family: Calibri, sans-serif;" class=""> 42 TAO, Function value: -2., Residual: 1.70295e-41<o:p class=""></o:p></div></div><div class=""><div style="margin: 0in 0in 0in 0.5in; font-size: 11pt; font-family: Calibri, sans-serif;" class=""> 43 TAO, Function value: -2., Residual: 1.70295e-42<o:p class=""></o:p></div></div><div class=""><div style="margin: 0in 0in 0in 0.5in; font-size: 11pt; font-family: Calibri, sans-serif;" class=""> 44 TAO, Function value: -2., Residual: 1.70295e-43<o:p class=""></o:p></div></div><div class=""><div style="margin: 0in 0in 0in 0.5in; font-size: 11pt; font-family: Calibri, sans-serif;" class=""> 45 TAO, Function value: -2., Residual: 1.70295e-44<o:p class=""></o:p></div></div><div class=""><div style="margin: 0in 0in 0in 0.5in; font-size: 11pt; font-family: Calibri, sans-serif;" class=""> 46 TAO, Function value: -2., Residual: 1.70295e-45<o:p class=""></o:p></div></div><div class=""><div style="margin: 0in 0in 0in 0.5in; font-size: 11pt; font-family: Calibri, sans-serif;" class=""> 47 TAO, Function value: -2., Residual: 1.70295e-46<o:p class=""></o:p></div></div><div class=""><div style="margin: 0in 0in 0in 0.5in; font-size: 11pt; font-family: Calibri, sans-serif;" class=""> 48 TAO, Function value: -2., Residual: 1.70295e-47<o:p class=""></o:p></div></div><div class=""><div style="margin: 0in 0in 0in 0.5in; font-size: 11pt; font-family: Calibri, sans-serif;" class=""> 49 TAO, Function value: -2., Residual: 1.70295e-48<o:p class=""></o:p></div></div><div class=""><div style="margin: 0in 0in 0in 0.5in; font-size: 11pt; font-family: Calibri, sans-serif;" class=""> 50 TAO, Function value: -2., Residual: 1.70295e-49<o:p class=""></o:p></div></div><div class=""><div style="margin: 0in 0in 0in 0.5in; font-size: 11pt; font-family: Calibri, sans-serif;" class=""> 51 TAO, Function value: -2., Residual: 1.70295e-50<o:p class=""></o:p></div></div><div class=""><div style="margin: 0in 0in 0in 0.5in; font-size: 11pt; font-family: Calibri, sans-serif;" class=""> 52 TAO, Function value: -2., Residual: 1.70295e-51<o:p class=""></o:p></div></div><div class=""><div style="margin: 0in 0in 0in 0.5in; font-size: 11pt; font-family: Calibri, sans-serif;" class=""> ^C</div></div></blockquote></blockquote></div></div></blockquote></div><br class=""></div></body></html>