[Scip] SCIP for mixed integer quadratic programming

[Mengda Wu]

Hi Stefan,

   Thank you so much for your reply!

   Can I programmably specify the quadratic objective function? I know
SCIPcreateVar has a parameter to add coefficients for linear objective
function. What should I do for quadratic objective function?

   Also, for the matrix in quadratic objective function, can I take any
advantage if it is sparse?

Thanks,
Mengda

On Mon, Feb 25, 2013 at 4:57 AM, Stefan Vigerske
<stefan at math.hu-berlin.de>wrote:

> 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<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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>
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