[Ipopt] about filter

[Andreas Waechter]

Hi RT,

> What is maximum number of entries in filter (a common value)? Is essentially
> action of filter function of maximum number of entries?

There is no maximal number of filter entries in the Ipopt implementation. 
It uses a std::list, which can get as long as it needs to.

You also sent a message directly to me - in the future, please send those 
questions to the Ipopt mailing list, since others might want to know about 
the answer as well, and someone else might also be able to answer faster 
than me (I also have a day job, that sometimes limits the amount of time I 
have for answering messages here... :-) ).

> Could you please give your opinion
> 
> What is your idea about multi-dimensional filters?
> 
> If we have different class of constraint set (e.g. some related to
> PDE solution, some on PDE coefficient, etc.), is it better to use
> multi-dim filter (add a dim for each set)?

In my mind, one of the advantages of a filter is that it might accept 
trial points more easily during the line search than a penalty methods 
does.  But in some circumstances, the filter can actually be more 
restricting, and sometimes (e.g., when the steps computed are not always 
very good, for example, when the problem is too nonlinear or one uses a 
quasi-Newton approximation) being too liberal in terms of accepting trial 
points can lead the optimizer to a bad area.

As you might know, some work has been done on looking at 
higher-dimensional filter methods, e.g.,:

http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=SJOPE8000016000002000341000001&idtype=cvips&gifs=yes

Here, one has one filter entry for not just all constraints combined, but 
for subsets of constraints separately, as you suggest.  For unconstraint 
optimization (here using the gradient entries as the filter components, 
not constraints), they report encouraging results.

I'm not sure how much you would gain in the Ipopt context.  It might make 
sense if you observe that many of the trial steps are rejected in the line 
search.  But then you might want to also understand why that is...

Instead of having more than one filter component for the constraints, you 
might also just want to reset the filter more often (see the 
filter_reset_trigger and max_filter_resets options).  But it probably 
won't help much.

Anyway, a higher-dimensional filter is not implemented in Ipopt, and it 
would not be a trivial change (beside writing the code for having a higher 
dimensional filter, you would also have to define an interface for the 
user to specify the subset of constraints that are to be taken together). 
But Ipopt is open source software, so you can go ahead an change it, and 
if it works great and is a good implementation, and you can contributed to 
an open source project (see 
http://www.coin-or.org/contributions.html#contributions), we could in the 
end add this to the Ipopt distribution... :-)

Regards,

Andreas