[SCIP] Solving a Convex MINLP

Mon Mar 9 17:51:12 CET 2026

Dear SCIP team and SCIP users,
A few months ago I asked if it was possible to solve a problem where all constraints were convex but some variables were integer (so relaxing these integral variables to intervals would make the problem convex).

SCIP provides a "constraints/nonlinear/assumeconvex" parameter that tells the solver "whether to assume that any constraint in the presolved problem is convex".

In my problem, if this parameter was False (default), constraints were not recognized as convex and SCIP entered into an expensive and useless spatial branch-and-bound.
If this parameter was True, however, SCIP gave integer solutions that were clearly suboptimal.

Stefan took some time to give me a very clear answer, and I wanted to share it here in case other people may face the same issue.

The problem was coming from SCIP's pre-processing that was breaking the convexity of my constraints : namely, one of the preprocessings replaces expressions like x^2 by x if x \in {0,1} - which is equivalent in {0,1}. This preprocessing may break the convexity of a constraint - for instance x^2/(y+1) < 1 is convex on [0,1]^2 but after running the preprocessing it becomes x/(y+1)<1 which is not convex anymore.

So Stefan pointed to such preprocessings and suggested to add something like "if assumeconvex == False" in their conditions to avoid destroying convexity ; after doing the correct change the solver works perfectly (cf. discussion below for more details).

Thanks for your help (and hopefully this message will help some other users!)
Guillaume

________________________________
De : Stefan Vigerske <svigerske at gams.com>
Envoyé : samedi 16 août 2025 12:50
À : Guillaume BS <guillaume_bs at hotmail.com>
Objet : Re: [SCIP] Solving a Convex MINLP

Hi,

thanks, I think I can reproduce and explain.
The assumeconvex parameter itself is odd. It tells SCIP that something
is convex, but doesn't explain why that is the case, and what is
necessary to preserve convexity. SCIP applies this to the presolved
problem, but the presolve reductions do not care about it and could
possibly destroy the convexity. It would be best not to use this
parameter, unless one knows exactly what is going on.

Looking at the problem, it's quite easy to guess where things go wrong:
You have binary variables z_0_0_ and terms z_0_0_^2 in the nonlinear
constraints. SCIP simplifies this to z_0_0_, which then destroys
convexity of the constraint function. There is no parameter to turn this
off. If you are happy to change code, then remove this part:
https://github.com/scipopt/scip/blob/80c1fbfe1b38cf92132630654bdf0998df8dd9e7/src/scip/expr_pow.c#L1440-L1445
If I do this, then the "MIP" problem seems to be solved correctly.

For the relaxed problem, replacing z_0_0_^2 by z_0_0_ is not possible
for SCIP, so you don't see the same issue.

Best,
Stefan

On 04/08/2025 17:17, Guillaume BS wrote:
> Hi Stefan,
> Thanks for your answer.
> Indeed exporting the nonlinear program with the ".cip" format allows easy communication of non-linear models between the C API and the SCIP command-line interface.
>
> I could reproduce the behavior observed in C: with the parameter "constraints/nonlinear/assumeconvex" to TRUE, SCIP converges to a suboptimal solution - while setting this parameter to FALSE leads to the true solution.
> On another hand, the fractional relaxation of the problem (with binary variables relaxed in [0,1] instead of {0,1}) is solved correctly even with assumeconvex = TRUE.
>
> I attached an example to this email with both the MIP and relax problems. Note that the non-linear constraints, lines 97 to 111, are convex (it is a direct implementation of constraints 9.c in https://www.researchgate.net/profile/Gerard-Cornuejols/publication/225470397_Mixed-integer_nonlinear_programs_featuring_onoff_constraints/links/0deec5213623630b0e000000/Mixed-integer-nonlinear-programs-featuring-on-off-constraints.pdf?_sg%5B0%5D=started_experiment_milestone&_sg%5B1%5D=started_experiment_milestone&origin=journalDetail ; computing the hessian also shows convexity).
>
> This behavior tends to show something odd with the assumeconvex parameter when used in a branch-and-bound tree.
> Do you confirm this interpretation – and, if so, do you know where it could come from ?
>
> Many thanks,
> Guillaume
>
>
>
> ________________________________
> De : Stefan Vigerske <svigerske at gams.com>
> Envoyé : lundi 21 juillet 2025 11:09
> À : Guillaume BS <guillaume_bs at hotmail.com>
> Objet : Re: [SCIP] Solving a Convex MINLP
>
> Hi,
>
> The reading/writing situation sounds not so good. There is some work in
> progress to add nl writing, but not sure it will make it into SCIP 10.
> For gms, there is a reader in the COIN-OR/GAMSlinks project, but it
> needs GAMS to run. OSiL writing is something that technically wouldn't
> be hard to do, but noone found the time.
> Anyway, yhou could try writing in SCIP's own CIP format. For that one,
> SCIP can write and read nonlinear constraints as well.
>
> Stefan
>
> On 21/07/2025 11:00, Guillaume BS wrote:
>> Dear Stefan,
>>
>> Thanks a lot for your answer, and for confirming this was not the intended behavior.
>>
>> The MINLP displaying this strange behavior was created with the C/C++ inteface of SCIP ; it contains several non-linear constraints (containing sum of fractions known to be convex).
>>
>> In order to better understand the problems and ensure there is no bug on my side/provide a reproductible example, I try to export the problem to a file to run it with SCIP command line interface.
>>
>> I could export a gms file (with the SCIPwriteGms function), but this format is not read by SCIP.
>> Conversly, it seems SCIP could read the OSiL format, but not export models in it.
>> I could not find any format for "generic" MINLPs - containing the nonlinear expressions provided by SCIP - that SCIP could both read and write. Do you know how one can export a nonlinear model created with the SCIP C++ interface and read it in the CLI ?
>>
>> Thanks again for your time,
>> Guillaume
>> ________________________________
>> De : Scip <scip-bounces at zib.de> de la part de Stefan Vigerske <svigerske at gams.com>
>> Envoyé : dimanche 13 juillet 2025 19:02
>> À : scip at zib.de <scip at zib.de>
>> Objet : Re: [SCIP] Solving a Convex MINLP
>>
>> Hi,
>>
>> constraints/nonlinear/assumeconvex only overwrites the convexity check
>> for nonlinear functions. So any g_i(x,y) is assumed to be convex in
>> (x,y) on the domain given by the variable bounds. So if this can be
>> assumed for y in [0,1], it will also work for y in {0,1}.
>> Maybe there is some bug which results in an incorrect solution for the
>> MINLP case.
>>
>> Stefan
>>
>>
>> On 07/07/2025 13:19, Guillaume BS wrote:
>>> Dear SCIP team,
>>>
>>> I am trying to solve a relatively simple convex MINLP of the shape:
>>>
>>> min c^t x
>>> s.t.:    g_i(x,y) \leq 0      i \in 1..m
>>>               Ax + By \leq d
>>>               x \in R^n, y \in B^n'
>>>
>>> with all functions g_i convex (cf "Convex MINLP" in https://www.scipopt.org/doc/html/WHATPROBLEMS.php ).
>>> I try to solve the MINLP (with variables y in {0,1}, and its convex relaxation (with variables y in [0,1]   ).
>>>
>>> In the documentation, a parameter "constraints/nonlinear/assumeconvex" is described, which allows assuming that all constraint functions are convex.
>>>
>>> The convex relaxed NLP with y \in [0,1]:
>>>
>>>      *
>>> is easily solved by SCIP when the  "constraints/nonlinear/assumeconvex" parameter equals TRUE
>>>      *
>>> is not easily solved by SCIP (several minutes for a toy instance with a few variables and constraints) when  "constraints/nonlinear/assumeconvex" equals FALSE ;  from the logs, it seems SCIP can't prove the complexity of the constraints and runs a spatial branch-and-bound (several nodes are generated, despite having only continuous variables).
>>>
>>> The MINLP with y \in {0,1}:
>>>
>>>      *
>>> is not correctly solved when "constraints/nonlinear/assumeconvex" is true: a feasible solution, with values of the binary variable y fixed "randomly", is returned by SCIP.
>>>      *
>>> is very slow when "constraints/nonlinear/assumeconvex" is false
>>>
>>> So it seems the  "constraints/nonlinear/assumeconvex" parameters not only controles the convexity of the constraints in the NLP relaxation, but also the convexity of the variables' domains - which would make it improper to solve an MINLP.
>>>
>>> Is this understanding correct and, if so, is there a way to solve a MINLP when all constraints are known to be convex - but the variables domain isn't ? (for instance by stating, for each nonlinear constraint, that it should be considered as convex?)
>>>
>>> Many thanks,
>>> Guilaume
>>>
>>>
>>> _______________________________________________
>>> Scip mailing list
>>> Scip at zib.de
>>> https://listserv.zib.de/mailman/listinfo/scip
>>
>> _______________________________________________
>> Scip mailing list
>> Scip at zib.de
>> https://listserv.zib.de/mailman/listinfo/scip
>>
>
>

-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://listserv.zib.de/pipermail/scip/attachments/20260309/3b7a1230/attachment.html>