[Coin-ipopt] Question on quadratic programming

[Andreas Waechter]

Hi Bo,

Thanks - I hope you (and everyone else reading the Ipopt mailing list) had 
some nice holidays, too!



In principle, you can use Ipopt to solve QPs, even though the default 
settings are not tuned towards QPs.

If you want to solve convex QPs, i.e., problems where the objective 
Hessian is positive definite (or at least positive definite in the null 
space of the constraints Jacobian),  you can run Ipopt with the options

mu_strategy monotone
mu_oracle probing

which make it run more like typical interior point QP solvers, and if you 
choose

corrector_type affine

it becomes pretty much the Mehrotra predictor-corrector method.

However, typically, specialized QP solvers choose the starting point in a 
clever way, while in Ipopt the user has to provide the starting point 
(since it is very difficult for general NLPs to determine a good starting 
point automatically, and we expect the user to give Ipopt some help here). 
I would suggest to choose a starting point that is not is not very close 
to the bounds (since this is bad for interior point methods), and you 
might want to play with the options

bound_push
bound_frac

Having said all this, Ipopt will probably not compete 100% with 
specialized solvers (depends on the solver of course :), which might be 
able to handle certain degeneracies etc, and also might avoid some 
overhead.

Why not just give it a try? :)  We tried (almost) everything to make the 
installation simple.

I hope this helps,

Andreas


On Sat, 23 Dec 2006, Bo Zhou wrote:

> Hi guy,
>
> I just found Ipopt recently and it looks fantastic. I'm wondering if I use it 
> for quadratic problems how is the performance looking? Will it compete those 
> specialized QP interior point solvers?
>
>
> Thanks, and have a nice holiday!
>
> Bo
>
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