It depends on the problem you are trying to solve. If at anytime, the hessian condition number ( <a href="http://en.wikipedia.org/wiki/Condition_number">http://en.wikipedia.org/wiki/Condition_number</a> ) is large then small variation can explode into something entirely different. At that point, numerical error (which is unavoidable when dealing with computer floating point) can play a significant role. Good linear solvers deal with these problems better than the others. If your problem is "well-behaved" then I think the performance will be less dependant on the choice of linear solver.<br>
<br><br><div class="gmail_quote">On Fri, Feb 17, 2012 at 9:17 AM, Joel Andersson <span dir="ltr"><<a href="mailto:joel.andersson@esat.kuleuven.be">joel.andersson@esat.kuleuven.be</a>></span> wrote:<br><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">
Hello!<br><br>I have often seen a large difference in performance of Ipopt, not just in the time per iteration, but in the number of iterations between the different linear solvers.<br><br>Do you have a simple explaination for this? I mean, since they are all direct sparse linear solvers, one would expect the linear system to be solved with high accuracy, and then it shouldn't really matter for Ipopt, which solver is used.<br>
<br>With some kind of iterative refinement of the solution, would you then expect all of the solvers to perform equally (again, not in terms of time, but in the steps taken)?<br><br>Best,<br>Joel<span class="HOEnZb"><font color="#888888"><br>
<br>-- <br>Joel Andersson, PhD Student<br>
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<br></blockquote></div><br><br clear="all"><br>-- <br>--------------------------------------------------<br>Binh Nguyen<br>Computer Science Department<br>Rensselaer Polytechnic Institute<br>Troy, NY, 12180<br>--------------------------------------------------<br>