[Scip] SCIP for mixed integer quadratic programming

[Stefan Vigerske]

Hi,

If you use SCIP as callable library, then you have to reformulate a 
nonlinear objective into a constraint by yourself:
min xQx  ->   min z  s.t. z >= xQx

For SCIP, it is absolutely advantageous, if the coefficient matrix is 
sparse.

For examples on how to setup a quadratic constraint, see example string 
in the Callable Library Example,
http://scip.zib.de/doc/examples/CallableLibrary/string_8c.shtml
or the .lp or .mps readers.

Stefan

On 02/25/2013 08:28 PM, Mengda Wu wrote:
> 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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>>>
>>
>