[Ipopt] Do there exist some optimization problems which are impossible to solve?

[Lewis I]

Dear Andreas and all.

In the tutorial, it mentioned "the modeler should try to avoid formulations where some non-zero entries in the gradients are typically very small or very large. A rescaling can be done by multiplying an individual constraint function by some factor, and by replacing a variable xi by x' = c * xi for a constant c != 0". 
What does it mean? Can anyone provide some examples?
Thank you

Lewis



----- Original Message ----
From: Andreas Waechter <andreasw at watson.ibm.com>
To: Lewis I <lewis369lewis at yahoo.com>
Cc: ipopt at list.coin-or.org
Sent: Sat, February 27, 2010 4:23:16 AM
Subject: Re: [Ipopt] Do there exist some optimization problems which are impossible to solve?

Hi Lewis,

This is a difficult question to answer in such generality.  As a guideline, you might want to try different ways to formulate your constraints, see, e.g., section 8 in the short Ipopt tutorial

http://drops.dagstuhl.de/volltexte/2009/2089/pdf/09061.WaechterAndreas.Paper.2089.pdf

Also, you might help the optimizer by trying different starting points, e.g., try to give it a feasible point.

To some degree, properly modeling a nonlinear nonconvesx optimization problem i na way that makes it easy to solve (or solve at all) is an art, and requires some time and experience.

Andreas

On Thu, 25 Feb 2010, Lewis I wrote:

> Dear All,
> 
> I have tried to use ipopt to solve some problems for a long time, but it always failed when I increase the number of constraints.
> I know it may be my own implementation problem, but I just wondering that do there exist some optimization problems which are impossible to solve in nowadays optimization technology?
> And these problems obj function and constraints are reasonable in reality.
> Please tell me if you know the answers.
> If yes, I will try to avoid those things.
> I would very appreciate if someone can help me.
> Thank you for your kind attention.
> 
> Regards,
> Lewis
> 
> 
> 
> 
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