Linear transformation based solution methods for non-convex mixed integer quadratic programs

Two preprocessing techniques for mixed integer quadratic programs with non‐convex objective functions are presented. The first is a convexification scheme and can be applied to problems were the continuous part of the Hessian is positive semidefinite. The second technique aims to reduce the size of the underestimating problems solved by branch‐and‐bound algorithms and can be applied to problems were the continuous part of the Hessian is singular. Numerical results are presented showing the effect of the preprocessing techniques.