Extreme strong branching for QCQPs

We propose extreme strong branching , which evaluates multiple branching points per continuous variable and jointly selects both the branching variable and point based on the objective value improvement. This approach resembles the success of strong branching for MIPs while additionally exploiting bound tightening as a byproduct. For certain types of quadratically constrained quadratic programs (QCQPs), computational experiments show that the extreme strong branching rule outperforms existing commercial solvers.