[Scip] Bilinear Constraints

[Todd Niven]

Thanks Stefan. SCIP is full of good surprises :-)

On 30 November 2011 05:09, Stefan Heinz <heinz at zib.de> wrote:
> Hi Todd,
>
> Just clear your final question. SCIP found the global optimal solution.
>
> Best Stefan
>
> On 11/29/2011 10:30 AM, Timo Berthold wrote:
>>
>> Hi Todd.
>>
>> Congrats, you found an optimal solution for your problem.
>> The warning that you get only states that SCIP cannot detect whether the
>> bilinear function is convex (concave) or not. This is done by testing the
>> matrix for positive (negative) semidefiniteness wherefor the eigenvalues
>> have to be computed. If a quadratic function is convex, one can use better
>> cuts and does not have to use underestimators, which often makes a big
>> difference in running time. However, SCIP solves the problem to global
>> optimality (if it solves it ;) ) in any case.
>>
>> If you are satisfied with SCIP's performance, nothing has to be done.
>> Elsewise, you can install IPOPT (www.coin-or.org/Ipopt) and compile SCIP
>> with IPOPT=true (or use a precompiled binary from the SCIP homepage that
>> contains IPOPT). This automatically gives you LaPack and might even help
>> for nonconvex problems, since some heuristics benefit from having an NLP
>> solver present.
>>
>> Cheers, Timo
>>
>>
>>> I have a model involving bilinear constraints (indeed the objective
>>> function is a sum of bilinear terms) in flatzinc format. When solving
>>> with SCIP, the following output is presented:
>>>
>>> "Quadratic constraint handler does not have LAPACK for eigenvalue
>>> computation. Will assume that matrices (with size>  2x2) are
>>> indefinite."
>>>
>>> Then SCIP continues to solve and eventually halts saying optimal
>>> solution found. My question is this: has SCIP only found a local
>>> optimal solution? If so, is there a way that SCIP can find global
>>> optimal solutions for MIPs with bilinear constraints?
>>>
>>> Thanks in advance.
>>>
>>> Todd Niven
>>> _______________________________________________
>>> Scip mailing list
>>> Scip at zib.de
>>> http://listserv.zib.de/mailman/listinfo/scip
>>>
>> _______________________________________________
>> Scip mailing list
>> Scip at zib.de
>> http://listserv.zib.de/mailman/listinfo/scip
>
>