Hello,<br><br>We, at ASCEND Team, have been adding support to use IPOPT for NLP problems in the past few weeks. Now that the solver is fully integrated with ASCEND, we tested both limited-memory and exact means of calculation of the lagrange of the hessians. In the process, we observed that limited-memory approach needed lesser number of iterations than exact hessians approach.<br>
<br>I've posted the median of a series of runs with both limited-memory and exact hessians below:<br><br>EXACT HESSIAN<br>------------------------<br><br>Number of objective function evaluations = 46<br>Number of objective gradient evaluations = 29<br>
Number of equality constraint evaluations = 0<br>Number of inequality constraint evaluations = 46<br>Number of equality constraint Jacobian evaluations = 0<br>Number of inequality constraint Jacobian evaluations = 29<br>
Number of Lagrangian Hessian evaluations = 28<br>Total CPU secs in IPOPT (w/o function evaluations) = 0.040<br>Total CPU secs in NLP function evaluations = 0.008<br><br>NUMERICAL HESSIAN<br>
--------------------------------<br><br>Number of objective function evaluations = 40<br>Number of objective gradient evaluations = 23<br>Number of equality constraint evaluations = 0<br>
Number of inequality constraint evaluations = 40<br>Number of equality constraint Jacobian evaluations = 0<br>Number of inequality constraint Jacobian evaluations = 23<br>Number of Lagrangian Hessian evaluations = 0<br>
Total CPU secs in IPOPT (w/o function evaluations) = 0.064<br>Total CPU secs in NLP function evaluations = 0.000<br> <br><br>Observe that the number of objective function,gradient function,etc evaluations in the Exact means is higher than numerical Hessians method.<br>
<br> It
seems likely that IPOPT could be using the data from the numerical hessian<br>evaluation to reduce the number of gradient evaluations,etc although usually one would expect the lower accuracy of numerical derivatives to slow down the convergence (i.e.) more number of iterations. Is something like that happening here?<br>
<br>Thanks,<br><br>Mahesh<br><br>-- <br>Developer<br>ASCEND Project<br><a href="http://ascendwiki.cheme.cmu.edu" target="_blank">http://ascendwiki.cheme.cmu.edu</a><br>