[Scip] Branching on continuous variables in the quadratic constraint

[Wen-Yang Ku]

Hi,

I have a mixed integer quadratic programming problem and I am running  
default SCIP without IPOPT. The variables (W_j) in the quadratic  
constraint are all continuous variables. These continuous variables  
are then linked with other integer variables by linear equality  
constraints. In the paper "Extending a CIP framework to solve MIQCPs"  
by Stefan, section 3.4 mentions that a spatial branching operation is  
performed to resolve infeasibility in a non-convex quadratic  
constraint, which is performed after all integer variables take an  
integral value in the LP optimum. My question is that, is it still  
algorithmic correct if I set the branching priority of these  
continuous variables (W_j) higher, in order to make SCIP branch on  
them before branching on the integer variables?

By the way, I noticed that compiling with IPOPT does not improve the  
performance for my problem. Is there a general guideline on the  
advantage (other than finding feasible solutions) using IPOPT?

Thanks,
Wen-Yang