[SCIP] Get auxiliary variables from reformulated expression graph

[liding xu]

Hi Stefan,
   Thank you for answering my questions and posting the document. It is
good news that scip will provide
   1. more control over the expression graph.
   2. more automatic reformulation.
   I want to do some experiments on the expression graph for the research
purpose, can you please send me the still-in-development version?

Best regards,
Liding

Stefan Vigerske <svigerske at gams.com> 于2021年6月14日周一 上午10:09写道：

> Hi,
>
> SCIP does this reformulation during presolve. cons_nonlinear adds new
> variables and changes constraints of the transformed problem. It doesn't
> really keep record of variables and constraints that are added during
> the reformulation, so there is no function to get these auxiliary
> variables or to get the constraints that were added. Their name
> typically starts with nlreform, though.
>
> For the signomial function, auxiliary variables are only introduced for
> the terms that aren't linear or quadratic. As said, there is no function
> that takes the parameters of the signomial and returns you some variable
> or constraint. But you could look through the constraints of the
> transformed problem which name starts with nlreform and that are of the
> form 0 <= signomial-term - nlreformxy <= 0. "signomial-term" is here an
> expression graph node of type polynomial (should probably better be
> named signomial) that has only one monomial or of type product. However,
> if the signomial term is neither convex nor concave, then it is
> reformulated further: Factors x_j^{p_{ij}} are replaced by new variables
> and products of more than two factors are split up.
>
> We have some code in development that replaces all this and would also
> make it easier to identify the signomial terms and corresponding
> auxiliary variables
> (https://www.scipopt.org/workshop2020/slides/minlp.pdf, starting with
> slide 9 or page 23). If you plan to do some work that builds on the
> handling of nonlinear constraints in SCIP and if you prefer to use this
> newer still-in-development version, then we can give you access to it.
>
> Stefan
>
> On 6/13/21 3:30 PM, liding xu wrote:
> > Dear SCIP community,
> >      I am aware that scip uses an expression graph to represent general
> > nonlinear functions and constructs its  linear under-estimators via
> > factorizable programming. Given a general nonlinear function (e.g.
> > signomial functions), scip adds auxiliary variables and constraints
> > associated with some intermediate nodes of the expression graph.
> >    I have the following common questions:
> >    1. In which phase (e.g. transformation, resolve), does scip
> reformulate
> > the expression graph to a set of auxiliary variables and constraints?
> >    2.How can get these auxiliary variables after reformulation, i.e.
> > (SCIP_VAR *) and constraints (SCIP_CONS*)?
> >    3. For example, given a signomial function f(x)  = \sum_i s_i(x),
> where
> > \sum_i s_i(x) =  c_i \prod_j x_j^{p_{ij}}.  how can I get the variable
> > associated to the signomial term s_i(x) = c_i \prod_j x_j^{p_{ij}}?
> >
> >   Best wishes,
> > Liding Xu
> >
> >
> > _______________________________________________
> > Scip mailing list
> > Scip at zib.de
> > https://listserv.zib.de/mailman/listinfo/scip
> >
>
>
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