In this talk, we discuss a general convex relaxation scheme via
D.C. decompositions for linearly constrained nonconvex quadratic
programming problems. We demonstrate an interesting equivalence between
the ``best'' parametric D.C. decomposition, in terms of the tightest convex
relaxation via D. C.decomposition, and its corresponding semidefinite relaxation
formulation. We gain dual benefits from the revealed property
between the SDP formulation and the best D.C. decomposition: (i)
Reduction of the iterative dual search process in finding the best
D.C. decomposition to a single SDP formulation, and (ii)
Identification of a feasible solution of the primal problem by
solving the convex relaxation corresponding to the SDP solution.
Three classes of special D.C. decomposition schemes, diagonal
perturbation, squared linear constraints, congruence transformation,
and their combinations are investigated. Preliminary numerical
results are reported to compare the tightness of the lower bounds
generated by different D.C. decompositions and other existing lower
bounds.