It is well known that semidefinite programming (SDP) can be used to derive useful relaxations for a variety of optimisation problems. Moreover, in the particular case of mixed-integer quadratic programs, SDP has been used to reformulate problems, rather than merely relax them. The purpose of reformulation is to strengthen the continuous relaxation of the problem, while leaving the optimal solution unchanged. In this paper, we explore the possibility of extending the reformulation approach to the (much) more general case of mixed-integer quadratically constrained quadratic programs.
This was eventually published as: L. Galli & A.N. Letchford (2014) A compact variant of the QCR method for quadratically constrained quadratic 0-1 programs. Optim. Lett., 8(4), 1213-1224.