[Scip] Optimal Multiplier Vector in Quadratic Programs

[Stefan Vigerske]

Hi,

no, SCIP might not even have computed dual multipliers internally for 
the quadratic constraints when finding an optimal solution.
If you have a (local) QCQP/NLP solver at hand, you could pass the 
solution from SCIP to it and let that solver compute a locally optimal 
dual solution for it.

If you want to dig into SCIP code, you could try to trigger an explicit 
call to Ipopt within SCIP after SCIP has finished the solve. The 
function solveSubNLP() in heur_subnlp.c may give an idea how to do this.
Essentially, you have to call SCIPtransformProb(), SCIPpresolve(), and 
SCIPsolve() (with a nodelimit of 1) to get into a state in which one can 
start a solve of the NLP relaxation (which isn't relaxing anything of 
your problem in your case) in SCIP. Then set the previously found 
solution via SCIPsetNLPInitialGuess() and solve the NLP with 
SCIPsolveNLP(). If that worked, you can query the rows of the NLP for 
their dual solution via SCIPnlrowGetDualsol(). Looking at the code in 
heur_subnlp.c, this sounded easier than it is :-).

Stefan

On 06/05/2015 11:45 AM, Apurv Shukla wrote:
> Dear All
> I am using SCIP as a black box solver for solving a nonconvex quadratically
> constrained quadratic program consisting of an indefinite quadratic
> objective, one quadratic equality constraint, one linear equality
> constraint  and box constraints on the variables. SCIP has been able to
> solve all the instances to optimality till now however since this is a part
> of a bigger primal-dual algorithm, I need the optimal multiplier vector
> (Lagrange Dual Vector) associated with each of the constraint at the
> optimal solution. Is there any method or procedure to retrieve these
> values? Any help regarding this will be much appreciated.
> Thanks
>
>
>
> Apurv Shukla
> Third Year Undergraduate Student
> Department of Mechanical Engineering
> IIT Kharagpur
> ᐧ
>
>
>
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