<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 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>