# [Ipopt] Slow convergence for simple problem

Andreas Waechter awaechter.iems at gmail.com
Wed Sep 21 17:29:45 EDT 2011

```Hi Swagato,

If you do not provide second derivatives to Ipopt, it uses a
quasi-Newton approximation, which is not the same as computing the
actual second derivatives, and can be much slower.  Since you have the
Hessian (C) available, I strongly suggest you write the code to return
it to Ipopt.

Andreas

On 09/20/2011 01:56 PM, Acharjee Swagato wrote:
> Hi Andreas,
> I checked the first derivatives using the derivative checker, there
> are no errors. I did not code the second derivative, so IPOPT is
> calculating it by itself. C is positive definite as I can solve the
> same problem using a quadratic optimizer.
> Swagato
>
> ------------------------------------------------------------------------
> *From:* ipopt-bounces at list.coin-or.org
> [mailto:ipopt-bounces at list.coin-or.org] *On Behalf Of *Andreas Waechter
> *Sent:* Tuesday, September 20, 2011 2:43 PM
> *To:* ipopt at list.coin-or.org
> *Subject:* Re: [Ipopt] Slow convergence for simple problem
>
> Hi Swagato,
>
> Did you verify that your coded the first and second derivatives
> correctly, using the derivative checker?  Is C positive definite?  (If
> not, Ipopt might something take a large number of iterations getting
> out of a nonconvex region)
>
> Andreas
>
>
>
> On 09/20/2011 07:40 AM, Acharjee Swagato wrote:
>> Hello IPOPT team,
>> I am a new user of IPOPT. I have a newbie question. I am trying to
>> solve a simple mean variance quadratic optimization problem of the form
>> min(X) - alpha*X + XCX'
>> I have some bounds on the variables and no other constraints. I am
>> using the ma27 solver with no hessian approximation.
>> For a 2500 variable problem I do not see IPOPT converging for 10-15
>> minutes for 3000+ iterations using default tolerance. As a comparison
>> I can solve the same problem using the quadprog library in R in much
>> less time. I am wondering what I am doing wrong.
>> Thanks,
>> Swagato
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> solicitation of any order to buy or sell. This communication,
> including any attachments, is for the exclusive use of the intended
> recipient(s) and/or the intended recipient's designees and may contain
> proprietary, confidential and/or privileged information. Any use,
> retention or dissemination by a person other than the intended
> recipient is strictly prohibited. If you are not the intended
> recipient or designee, please notify the sender immediately by return
> e-mail and delete/destroy all copies of this communication. Any
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