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Hi,<br>
<br>
If you solved the problem with Mosek, you must have provided the
Hessian matrix, correct? If so, why don't you give the Hessian also
to Ipopt? This will certainly improve convergence, at least in
terms of iteration counts. If you are using the L-BFGS option
because your Hessian is dense, you might want to play with the
"acceptable_" termination criteria. Finally, I would always use the
derivative checker to make sure the derivatives are indeed correct.<br>
<br>
Andreas<br>
<br>
<pre class="moz-signature" cols="72">
</pre>
<br>
On 03/22/2012 09:05 PM, paras tiwari wrote:
<blockquote
cite="mid:CAFHBpLo62J6h0v5sYRnXMjSNOjKTtx_HoN77e71caA16dVnFmA@mail.gmail.com"
type="cite"><span style="font-family:Tahoma;font-size:13px">Hello,</span>
<div style="font-family:Tahoma;font-size:13px"><br>
</div>
<div style="font-family:Tahoma;font-size:13px">I was trying to
solve a quadratic convex optimization problem in IPOPT. The
objective function is quadratic and convex, and I was using
limited-memory option to approximate hessian. The objective
function value was decreased rapidly at the beginning, but it
decreased slightly in later iterations. IPOPT did not converge,
and it either stopped at maximum iteration or threw
"Restoration phase Failed" error. I solved the same problem
using Mosek, and it's pretty fast and it converged at the global
minimum. Any suggestion would be highly appreciated.</div>
<div style="font-family:Tahoma;font-size:13px"><br>
</div>
<div style="font-family:Tahoma;font-size:13px">Thank You,</div>
<div style="font-family:Tahoma;font-size:13px">Paras</div>
<div style="font-family:Tahoma;font-size:13px">
<br>
</div>
<div style="font-family:Tahoma;font-size:13px">
<div>Here is </div>
<div>
<div><br>
</div>
<div><br>
</div>
<div>******************************************************************************</div>
<div>This program contains Ipopt, a library for large-scale
nonlinear optimization.</div>
<div> Ipopt is released as open source code under the Common
Public License (CPL).</div>
<div> For more information visit <a
moz-do-not-send="true"
href="http://projects.coin-or.org/Ipopt">http://projects.coin-or.org/Ipopt</a></div>
<div>
******************************************************************************</div>
<div><br>
</div>
<div><br>
</div>
<div>Number of nonzeros in equality constraint Jacobian...:
0</div>
<div>Number of nonzeros in inequality constraint Jacobian.:
205361</div>
<div>Number of nonzeros in Lagrangian Hessian.............:
0</div>
<div><br>
</div>
<div><br>
</div>
<div>Total number of variables............................:
1092</div>
<div> variables with only lower bounds:
0</div>
<div> variables with lower and upper bounds:
1092</div>
<div> variables with only upper bounds:
0</div>
<div>Total number of equality constraints.................:
0</div>
<div>Total number of inequality constraints...............:
1489</div>
<div> inequality constraints with only lower bounds:
0</div>
<div> inequality constraints with lower and upper bounds:
0</div>
<div> inequality constraints with only upper bounds:
1489</div>
<div><br>
</div>
<div>iter objective inf_pr inf_du lg(mu) ||d||
lg(rg) alpha_du alpha_pr ls</div>
<div> 0 2.0230492e+03 0.00e+00 1.75e+01 0.0 0.00e+00 -
0.00e+00 0.00e+00 0</div>
<div> 1 1.6490451e+03 4.26e-14 1.45e+01 -4.5 3.54e+00 -
1.69e-02 1.00e+00f 1</div>
<div> 2 1.1222267e+03 5.68e-14 8.02e-01 0.5 2.09e+01 -
9.58e-01 1.00e+00f 1</div>
<div> 3 7.7570431e+02 8.53e-14 4.20e+00 -0.0 1.20e+01 -
9.94e-01 1.00e+00f 1</div>
<div> 4 4.1287003e+02 6.39e-14 7.19e+00 -0.8 2.54e+01 -
8.28e-01 8.38e-01f 1</div>
<div> 5 5.3114831e+01 8.79e-14 9.83e-01 -6.4 2.09e+01 -
3.64e-01 8.05e-01f 1</div>
<div> 6 2.5938399e+01 1.18e-13 1.90e-02 -2.8 4.56e+00 -
9.02e-01 9.99e-01f 1</div>
<div> 7 2.5857683e+01 1.20e-13 2.78e-01 -2.8 4.18e+00 -
1.00e+00 3.94e-03f 1</div>
<div> 8 3.9173220e+01 1.14e-13 6.04e-01 -0.1 1.41e+02 -
7.19e-03 1.62e-02f 1</div>
<div> 9 2.7548619e+01 1.12e-13 3.09e-01 -1.9 5.36e+00 -
7.51e-01 3.91e-01f 1</div>
<div>A few last iterations are:</div>
</div>
<div>
<div>2992 1.2285442e+01 1.05e-13 3.90e-01 -6.2 2.34e-03 -
1.00e+00 2.78e-01h 1</div>
<div>2993 1.2285445e+01 8.53e-14 1.43e+00 -6.2 5.62e-02 -
3.08e-01 1.25e-01f 4</div>
<div>2994 1.2285445e+01 9.15e-14 1.32e+01 -6.2 2.77e-01 -
1.00e+00 3.90e-03f 4</div>
<div>2995 1.2285442e+01 1.06e-13 2.42e-01 -6.2 3.50e-03 -
1.00e+00 1.00e+00h 1</div>
<div>2996 1.2285441e+01 1.07e-13 7.47e-01 -6.2 2.15e-03 -
1.00e+00 1.00e+00h 1</div>
<div>2997 1.2285456e+01 7.28e-14 1.75e+00 -6.2 1.01e-02 -
1.00e+00 1.00e+00H 1</div>
<div>2998 1.2285456e+01 1.24e-13 2.47e+00 -6.2 1.95e-02 -
1.00e+00 9.31e-10h 31</div>
<div>2999 1.2285450e+01 1.02e-13 1.43e+00 -6.2 1.02e-02 -
3.85e-01 5.00e-01f 2</div>
<div>iter objective inf_pr inf_du lg(mu) ||d||
lg(rg) alpha_du alpha_pr ls</div>
<div>3000 1.2285450e+01 1.32e-13 1.10e+00 -6.2 9.22e-02 -
2.68e-01 2.05e-03h 6</div>
</div>
</div>
<br>
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<br>
<pre wrap="">_______________________________________________
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</pre>
</blockquote>
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