[SCIP] reformulations and convex MINLP

[Stefan Vigerske]

Hi,

both is still correct for SCIP 4.
One exception might be the disaggregation of SOC, which was added with 
SCIP 4.

There is also the recent paper
http://nbn-resolving.de/urn:nbn:de:0297-zib-59377
which at the beginning of Section 2.4.1 states that underestimators for 
each summand (f(x), g(x)) are computed and then summed up for a single 
cut. (my thesis should say the same somewhere)
Indeed, there are cases where splitting up the sum and adding additional 
auxiliary variables would be more efficient. One reason against it had 
to do with summing up of small violations of auxiliary constraints.

Looking forward to see your thesis :),
Stefan

On 04/14/2017 08:56 PM, Miles Lubin wrote:
> Dear SCIP experts,
> 
> I would like to accurately characterize SCIP's handling of convex MINLP for
> my thesis. The best reference I can find for how SCIP deals with convex
> MINLP is this 2012 ISMP talk (
> https://www.math.hu-berlin.de/~stefan/SCIP_ISMP12.pdf) by Stefan. Slide 9
> states that if a composition of functions f(g(x)) is known to be convex or
> concave, then no auxiliary variables are added. (This is in contrast to the
> nonconvex case where z = g(x) will be introduced.) Is this statement still
> accurate?
> If so, is it also the case that if a constraint is of the form f(x) + g(x)
> <= 0, and both f() and g() are heuristically detected to be convex, then no
> auxiliary variables are added?
> 
> Thanks!
> Miles
> 
> 
> 
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