[Scip] Bilinear Constraints

[Timo Berthold]

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
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