[Scip] SCIP for mixed integer quadratic programming

[Stefan Vigerske]

Hi,

usually the SCIP readers or interfaces take care of reformulating a 
nonlinear objective into a constraint, so you will not have to worry 
about it. The constraint handler for quadratic constraints is often able 
to recognize that its constraint was actually an objective function and 
gives some help on finding feasible solutions (these are the solutions 
that are marked by 'y' in the first column).

In order to have SCIP recognize that your quadratic constraint matrix is 
positive definite, you should build SCIP with Ipopt (SCIP uses Ipopt's 
Lapack interface to check the matrix for positive semidefiniteness). The 
availability of Ipopt also enables the solution of quadratic programs 
within some heuristics, which can be helpful if you have continuous 
variables in the quadratic part of your objective.

You could also check if one or both of the following parameter settings 
has an effect:
constraints/quadratic/replacebinaryprod = 0
constraints/quadratic/sepanlpmincont = 0

For information about which reader in SCIP can handle mixed integer 
quadratic programs, see
http://scip.zib.de/doc/html/group__FILEREADERS.shtml

Stefan

On 02/24/2013 11:59 PM, Mengda Wu wrote:
> Hi All,
>
>     I have a mixed integer problem with quadratic objective function with
> some linear constraints. The matrix in the quadratic is positive definite.
> I am wondering if/how well SCIP can handle this type of problem. I read
> some previous posts that it needs to be converted into quadratic
> constraints. I am trying to evaluate SCIP against some commercial
> libraries, e.g. CPLEX or GUROBI.
>
> Thanks,
> Mengda
>
>
>
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