Parabolic Relaxation for Quadratically-constrained Quadratic Programming -- Part I: Definitions & Basic Properties. (arXiv:2208.03622v1 [math.OC])

For general quadratically-constrained quadratic programming (QCQP), we
propose a parabolic relaxation described with convex quadratic constraints. An
interesting property of the parabolic relaxation is that the original
non-convex feasible set is contained on the boundary of the parabolic
relaxation. Under certain assumptions, this property enables one to recover
near-optimal feasible points via objective penalization. Moreover, through an
appropriate change of coordinates that requires a one-time computation of an
optimal basis, the easier-to-solve parabolic relaxation can be made as strong
as …

arxiv math part programming