Spectral Relaxations and Branching Strategies for Global Optimization of Mixed-Integer Quadratic Programs

We consider the global optimization of nonconvex (mixed-integer) quadratic programs. present a family convex relaxations derived by convexifying functions through perturbations matrix. investigate theoretical properties these and show that they are equivalent to some particular semidefinite also introduce novel branching variable selection strategies motivated investigated in this paper. The proposed relaxation techniques implemented solver BARON tested conducting numerical experiments on large collection problems. Results demonstrate implementation leads very significant reductions BARON's computational times solve test